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MANUAL OF LOGIC 



MANUAL OF LOGKLC, 



DEDUCTIVE AND INDUCTIVE. 






H. H. MUNEO, 



'• Since it is reason which sets in order and finishes all things, it ought not 
itself to be left in disorder." — Stoic. 






GLASGOW: MAURICE OGLE AND SON 

LONDON: HAMILTON, ADAMS AND CO. 

EDINBURGH: ROBERT OGLE. 

MDCCCL. 



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GLASGOW: 
PRINTER B T S. AND T. DUNN, 

14, Prince's Square. 



7rZ*L £* 'o^rnr-l &1~<L *-rx,ttf}< 



PREFACE. 



The object contemplated in the following pages is to 
present the tyro with a succinct, yet comprehensive, view 
of Logic in the simplest possible form. 

Instruction in Logic is now no longer confined to 
Colleges and Universities : it has been introduced into 
many of our schools and academies ; and it is hoped that 
an effort to simplify, without compromising, the distinc- 
tive characteristics of a study, so elegant in its nature, and 
so highly calculated to train the youthful mind to correct 
habits of thought, may not be unacceptable to the latter 
class of seminaries. 

The writer has been induced to this undertaking, from 
its having appeared to him, when employed as a tutor in 
Logic, that an elementary manual, more simple in its 
phraseology, and more copious in illustrations and ex- 
amples, than any of the treatises now in use, might 
tend, in some measure, to facilitate an earlier and easier 
acquaintance with the science than is at present at- 
tainable. 

In the hope of securing this object, the use of abstract 
symbols in illustration has been almost entirely dis- 

a2 



11 PREFACE. 

carded; for although convenient for the compiler of a 
logical treatise, and intelligible to the advanced student, 
they are invariably uninteresting, if not repulsive, to the 
beginner. 

Simplicity has been invariably adhered to, in selecting 
examples, alike in propositions and syllogisms ; but it is 
hoped that they are not of such a nature as to incur the 
charge of triviality, so frequently brought against works 
on Logic, owing to the meagreness of the illustrations 
usually employed. 

The conflicting views entertained, regarding the true 
province of Logic, surround the publication of an ele- 
mentary treatise with peculiar difficulties. Any person, 
however, who has duly considered the matter, can have 
little difficulty in deciding, that if Logic is to be consi- 
dered a distinct and self-sufficient scientific art, the for- 
mal view must be adopted ; for this is the only aspect 
under which its proper function can be adequately de- 
fined and defended. It is possible, however, that the 
disciples of the formal school, in their abhorrence of the 
material and verbal views, have somewhat overstrained 
their own theory ; and that, in order to arrive at a yet 
more satisfactory definition, they must either agree to a 
slight compromise, or reject, as extralogical, many mat- 
ters admitted at present into logical works. # 

In declaring his adhesion to the formal view of the 
province of Logic, the writer readily admits that he has 
introduced into the following pages much that is extra- 



PREFACE. Ill 



logical; and his apology is, that his object was not to 
vindicate any particular theory, but rather to lay before 
the tyro whatever seemed most useful as an introduction 
to the subject, more particularly as it has not as yet been 
determined to what special branch of knowledge matters 
now deemed extralogical are to be assigned. 

The discussion of vexed questions has been altogether 
excluded from the text, as their introduction seemed in- 
consistent with the plainness requisite in an elementary 
work; but when considered necessary, they have been 
adverted to in Notes. 

To the authors of the many very valuable works on 
Logic, which have recently emanated from Oxford, the 
writer gratefully acknowledges his obligations. The 
treatises alluded to are obviously intended to supply the 
defects and correct the errors of the University Text- 
book, with such additions as have seemed necessary to 
prepare students for the present high standard of logical 
examinations. But although extremely valuable in this 
respect, the works referred to have left the necessity of a 
work purely introductory unsupplied. 

The writer also willingly acknowledges the benefits he 
has derived from the unrivalled article by Sir W. Hamil- 
ton in the ' Edinburgh Eeview/ as may be seen from the 
ample use made of its contents throughout this Manual. 
To this article the more correct views of the province of 
Logic, recently adopted in this country, are mainly 
attributable. 



IV PREFACE. 

It was originally intended to treat of Inductive Logic 
at some length in this Manual; but the unexpected 
space -which Deductive Logic has occupied, has rendered 
a full consideration of it incompatible with the publish- 
ing arrangements of the present edition. 

Glasgow, January, 1850. 



CONTENTS. 



Page 

Introduction, ....... ix 

CHAPTER I. 

Section I. Heads of the Ancient Logic — Simple Apprehension, 
Judgment, Reasoning — General Explanation of this Division — 
Rationale of this Division — Notes, .... 1-4 



Section II. Definition of Simple Apprehension — Divided into In- 
complex and Complex — Incomplex Apprehension explained — 
Complex Apprehension explained — Simple Terms explained — 
Simple Terms may consist of one or more Words — Errors incident 
to Simple Apprehension, Judgment, and Reasoning — Terms de- 
fined — Divided into Simple, Complex, and Decomplex — Simple 
Terms — Categorematic, Syncategorematic, and Mixed — Simple 
Terms explained according to this Division — Complex Terms 
explained — Decomplex Terms explained — Definition of the Logical 
Term — The Logical Term divided into Singular and Common — 
Singular and Common Terms explained — Various Names appli- 
cable to Common Terms — Notes, . . . 4-24 

CHAPTER II. 

Section I. Abstraction explained and illustrated — Generalisation 

explained and illustrated — Nominalism and Realism — Notes, 24-32 



CONTENTS. 



Page 



Section II. Extension and Comprehension of Terms explained- 

Scheme of Extension and Comprehension, . . . 32-37 

Section III. The Predicables — General Explanation, with Exam- 
ples — Scheme of the Porphyrian Tree — Definition and Explana- 
tion of Genus — Definition and Explanation of Species — Scheme of 
Subaltern Genera and Infimse Species — Definition and Explana- 
tion of Differentia — Divided into Generic and Specific — Definition 
and Explanation of Proprium — Divided into Generic and Specific 
— Definition and Explanation of Accidens — Scheme of the Heads 
of Predicables, with their Subdivisions, . . . 37-62 

Section IV. The Categories or Predicaments — Enumeration of 
them — Aristotelic Enumeration adopted, as simplified by Sir W. 
Hamilton — Classifications of Locke, Hume, Kant, Mill, Thomson, 64-69 

Section V. Division — Rules of Logical Division — Logical Wholes 

of Extension and Comprehension — Boethius on Division — Notes, 69-75 

Section VI. Definition — Definition of two kinds — Nominal and 

Real — Rules of Definition — Aristotle's view of Definition, . 75-83 

Section VII. Of the Distribution of Terms— Of the Subject— Of 
the Predicate, ...... 83-88 

CHAPTER III. 

Section I. Judgment — Simple Propositions — Division of Proposi- 
tions — Substance of Propositions — Quality of Propositions — 
Quantity of Propositions — Notes, .... 89-104 

Section II. Modality of Propositions — Examination of Aristotle's 
four Modes, . . . . . . . 104-110 

Section III. The Opposition of Propositions— Subaltemation — 



CONTENTS. Vll 

Page 
Contrary Opposition — Sub-contrary Opposition — Contradictory 

Opposition — Opposition of Singular Propositions, . . 110-121 

Section IV. Conversion of Propositions — Simple Conversion — 
Conversion of Universal Negatives — Conversion of Particular 
Affirmatives — Conversion per Accidens — Conversion of Universal 
Affirmatives — Conversion of Universal Negatives — Conversion by 
Contraposition or Negation, ..... 122-130 

CHAPTER IV. 

Section I. Of Syllogism — Rules of Syllogism — Canons — Rules of 
Syllogism of two kinds — General and Special — General Rules 
explained and exemplified — Special Rules explained and exem- 
plified — Figures of Syllogism — Moods of Syllogism, . ^ 130-163 

Section II. Reduction of Syllogisms — Reduction, of two kinds — 
Direct and Indirect — Examples, .... 163-176 

Section III. Reductio per Impossible or ad Absurdum — Exam- 
ples — Compound Propositions, .... 176-186 

Section IV. Conditional Syllogisms — Disjunctive Syllogisms — 
Examples, ...... 186-192 

Section V. Of the Dilemma — Destructive and Constructive. 
Examples, ....... 192-201 

Section VI. Of the Enthymeme — Aristotelic view of the Enthy- 
meme — Ordinary view — Rules — Examples, . . . 201-208 

Section VII. Of the Epicheirema — Explanation — Examples, 208-210 

Section VIII. Of the Sorites — Its meaning as a species of argu- 
mentation-— Expanded into separate Syllogisms — Rules — Exam- 
ples — The Goclenian Sorites explained, . . . 211-218 



Vlll CONTENTS. 

Page 
Section IX. Of the Example — Different from Induction — Exam- 
ples, ....... 218-220 

Section X. Of Sophisms — Divided into Fallacies in the Expres-- 
sion, and Fallacies in the Matter — Both kinds explained and 
exemplified — Of Induction — Explained as understood by Aris- 
totle — Views of the nature of Induction examined — Aristotelian 
view adopted, 220-236 



INTKODUCTION 



The conflicting opinions entertained by writers on Logic, 
as to its proper province, and also as to whether it is an 
art or science, or both, verifies the adage — Omnis dejinitio 
periculosa est, Aristotle has unfortunately left us no de- 
finition of Logic ; and from the mixed nature of the con- 
tents of the Organon, it would certainly have been difficult 
to do so. 

That Logic is both a science and an art has always been 
admitted by every one acquainted with its proper province 
and nature. It is a science, inasmuch as by analysing 
the elements, principles, and structure of arguments, it 
teaches us how to discover their truths, or detect their 
fallacies, and point out the sources of such errors. It is 
an art, inasmuch as it teaches us to arrange arguments 
in such a manner as that their truth may be most readily 
perceived, or their falsehood detected. 

It would be out of place here to enter on an examina- 
tion of many definitions, as it would be an unprofitable 
encroachment on space that may be more usefully occu- 
pied. It is only intended, therefore, to consider briefly 
those of Dr Eeid, Archbishop Whateley, and Sir William 

Hamilton. 

b 



X INTRODUCTION. 

According to Eeid, the professed end of Logic is ' to 
teach men to think, judge, and reason, with precision and 
accuracy! This definition is evidently founded on the 
usual division of the cognitive faculties, and, on this ac- 
count, must be considered at least ingenious. 'To think' 
is obviously intended to refer to simple apprehension — 
'judge/ to judgment, mental or verbal — and 'reason,' to 
syllogism. But this distribution of the cognitive faculties 
is itself a cross- division, for the dividing members are not 
distinct. They run into one another, and consequently 
the same fault characterises the definition founded on 
them. Logic is certainly furnished with its own peculiar 
rules and canons ; but rules, in any science, can never be 
employed for the discovery or investigation of truth. Their 
sole use and end is to guard against error. If this de- 
finition were to be admitted, all known sciences might 
be at once stripped of their distinctive appellations, and 
be indiscriminately classed under the name — Logic. The 
grand error in this definition is, however, that it confounds 
the material with the logical; in other words, the process 
of investigation with the inference necessitated by the laws 
of thought. Logic has nothing to do with things as they 
exist really and in themselves, but only the forms of 
thought under which the mind conceives them. It is 
conversant solely about second, not Jirst notions. Hence, 
a logical inference is not determined by any objective 
casualty subsisting between the terms of the premisses 
and conclusion, but solely the subjective relation of reason 
and consequence under which they are construed to the 
mind in thought. The question whether the premisses 
of an argument in any objective science are true, is, no 
doubt, a very important one ; but the logician, as such, 
cannot be called upon to answer it. He may be able to 



INTRODUCTION. XI 

answer it, but it will be as an Astronomer, Chemist, Geo- 
logist, Botanist, &c, as the case may be, but not as a logi- 
cian ; for as a logician he is merely responsible for the 
soundness of the consequent on the assumed truth of the 
antecedent. The merit of the correct antecedent is ma- 
terial of the correct consequent logical. Cuique in sua arte 
credendum. 

In Archbishop Whateley's opinion, 'Logic is the art of 
employing language properly for the purpose of reason- 
ing.' This definition restricts the province of Logic to 
the regulation of language. It may be a slight improve- 
ment on the definition of Hobbes, viz., that Logic is 'the 
art of computation ' — a kind of mental arithmetic, not 
conducted by figures, but by words. We add, for in- 
stance, two terms to make an affirmation, two affirmations 
to make a syllogism, and many syllogisms to make a de- 
monstration. There is undoubtedly an intimate connec- 
tion between thought and language; but the regulation 
of language falls within the province of grammar, not of 
Logic ; for if it were, thought would necessarily be con- 
sidered a function of a language, instead of language 
being a function of thought. On this definition, the 
pointed remarks of Mr Chretien are conclusive : ' If 
thought be only a function of language, man is better 
characterised as a speaking than as a reasoning being; 
for it is more natural and more scientific to define by the 
cause than the effect. And then, to draw any such in- 
ference from man's possessing reason, as that his actions 
are therefore probably free, or his thinking nature im- 
mortal, becomes at once absurd ; for none will assert 
such liberty or immortality to be a consequence of speech, 
of which reason itself is on this theory a consequence.' a 

a Essay on Logical Method, by Charles P. Chretien, M.A., Oxford. 



Xll INTRODUCTION. 

Sir William Hamilton defines Logic to be ' the science 
of the laws of thought as thought — that is, of the neces- 
sary conditions to which thought, considered in itself, is 
subject. This is technically called its form' This defi- 
nition is probably intended as an improvement on that 
given by Kant, viz., c the science of the necessary laws of 
the understanding and the reason.' The definition of 
Kant may be simplified by the explanation, that the in- 
ferences of opposition and conversion are considered by 
him as syllogisms of the understanding, and the usual 
form of syllogisms as the syllogisms of the reason. Sir 
William Hamilton's definition is here adopted. 

In connection with this definition, the foregoing brief 
introductory remarks may be very appropriately closed 
with the following judicious passage from Mr Mansel: — 
'It is not intended to deny the usefulness of Logic ; but 
it may safely be asserted, that its more valuable fruits are 
to be found in the training which the mind unconsciously 
receives, than in the conscious employment of knowledge 
in the formation and examination of reasonings, and that 
both, in respect of the true character of the science, are 
secondary and accidental results — not primary and essen- 
tial features.' 



MANUAL OF LOGIC. 



CHAPTER L 
SECTION I. 



The ancient Logic consisted of three heads, viz., Simple 
Apprehension,* Judgment, and Reasoning. The earlier 
Logicians considered these, in so far as the province of Logic 
was concerned, as the only operations of the mind. From 
its convenience, this distribution of the cognitive faculties has 
still been followed. 

Under the first head, viz., Simple Apprehension, notions are 
treated of, and these notions, when expressed in words, are 
called simple terms. 

The second head, viz., Judgment, treated of the agreement 
or disagreement of any two notions, whether incomplex or 
complex, when compared together in the mind; and this 
comparison is termed a judgment, (a-ro^ai/cvc) and when 
verbally expressed, a ■proposition (Kgoraac). 

The third head, viz., Reasoning, treated of syllogism, or the 
manner in which, from two judgments or propositions related 

a There is no phrase in Aristotle exactly corresponding to simple apprehen- 
sion : the nearest is r\ ruv adiaigerwv vorjffig — the apprehension of uncom- 
pounded notions; vorjtfig is, however, not restricted to any specific meaning by 
Aristotle. 

A 



2 MANUAL OF LOGIC. 

to each other, the mind proceeds to a third judgment or 
proposition, founded upon and resulting from them. 

This division 11 of the mental powers, although objectionable, 
is at all events recommended by its simplicity. Its rationale 
is as follows : — 

1. We first acquire simple notions ; from these we proceed 
to notions of a more complex character, and to the mental 
faculty by which these two classes of notions are acquired 
we give the name, Simple Apprehension. 

2. In virtue of our mental constitution, when once pos- 
sessed of notions, we begin to compare them ; in other words, 
we institute mental judgments 1 * as to whether the notions or 
ideas we have acquired by simple apprehension, agree or 
disagree with each other ; and the judgments thus formed, 
when expressed in words, we term propositions. 

A proposition consists of a subject, predicate and copula. 
The subject is that of which something is affirmed or denied ; 
the predicate that which is affirmed or denied of the subject ; 
and the copula that which unites the subject and predicate; as 

Knowledge is power ; — 
or disjoins the subject and predicate ; as, 

Predacious animals are — not ruminant. 

a On this division Sir W. Hamilton remarks : — ' The division in question, I 
make bold to say, never was proposed by any philosopher, as a psychological 
distribution of the cognitive faculties in general ; on the contrary, it is only a 
hgical distribution of that section of the cognitive faculties which we denomi- 
nate discursive, as those alone which are proximately concerned in the process 
of reasoning or thought, in its strictest signification.' — ReioVs Works, p. 242. 

b Reid defines judgment to be an act of the mind whereby one thing is affirmed 
or denied of another. On this definition Mansell remarks very properly, 
( Rudimenta, p. 3) : ' Thing is vague enough ; but it is not easy to comprehend 
the various kinds of judgment under any more precise expression. The terms 
of a judgment are not always objects of perception, and the very notions of 
agreement and disagreement are the consequences of judgment, not the con- 
ditions of possibility. In fact, judgment is as necessary to apprehension as ap- 
prehension to judgment.' 



MANUAL OF LOGIC. 3 

The substantive verb, in the present tense, is the affirma- 
tive copula. With the negative particle not affixed, it con- 
stitutes the negative copula. The affirmative judgment is 
sometimes called composition (twdsas), because it unites the 
two conceptions compared. The negative is sometimes called 
division (diuigstfig), because, on the other hand, it separates 
the two conceptions compared. 

When comparing ideas, we find agreements to be either 
total or partial, and also disagreements to be either total 
or partial. Hence an affirmative proposition 4 may be either 
universal* or particular f and a negative proposition 5 also uni- 
versal or particular. 

3. In a syllogism we alternately compare two terms (the 
major and minor) with a third, called the middle term ; and 
in this way we ascertain whether the two terms, alternately 
compared with it, agree or disagree with each other. 

A regular syllogism consists of three propositions : the two 
first are called the premisses, and the last the conclusion. In 
the premisses, the two terms whose agreement or disagreement 
is sought to be proved, are compared with the middle term, 
and the new proposition resulting from them is called the 
conclusion, e. g. — 

Every effect is the result of an adequate cause. 

The world is an effect ; therefore, 

The world is the result of an adequate cause. 

No ruminant animals are predacious. 
The lion is predacious ; therefore, 
The lion is not a ruminant animal. 

This division of the cognitive faculties into three distinct 
parts does not imply that they are altogether independent of 
each other. A progressive connection exists between them ; 

a xaratpatftg — oratio affirmans. b za&oXov. 

c Kara, fisoog. d avrotpaffig — oratio negaus. 



* MANUAL OF LOGIC. 

and in the view of the logician, apprehension must be consi- 
dered in its reference to judgment, and judgment in its rela- 
tion to discourse/ 

All sciences have their technicalities, and without them no 
science would be intelligible. Apprehension, judgment, and 
reasoning, are the names by which logicians have agreed to 
express the faculties of obtaining evidence, whether intuitive 
or deductive ; and they stand to each other in the relation of 
simple, complex, decomplex. h 

It will be seen from the foregoing 

1. That a notion obtained by simple apprehension, when 
expressed in words, is called a term. 

2. That an act of judgment is expressed by a proposition; 
and, 

3. That an act of reasoning, when stated in regular form, 
is termed a syllogism. 

These three heads will be more fully illustrated in their 
proper places. 

a The relation subsisting between the three acts of thought is expressed in 
both these nomenclatures ; the one (simple, complex, decomplex) implying 
the synthetical advance from apprehension to judgment and discourse ; the 
other (syllogism, proposition, term) resolving, analytically, the complete and 
final act into its component judgments and apprehensions. — Woolley, p. 19. 

b In speaking of this division, Reid states (Inquiry, cap. 7) : — 'The second 
includes the first, and the third includes both the first and second, but the first 
may be exercised without either of the other two.' On this opinion Sir W. 
Hamilton remarks: 'Apprehension is as impossible without judgment as 
judgment is impossible without apprehension. The apprehension of a thing or 
notion is only realised in the mental affirmation, that the concept ideally exists; 
and this affirmation is a judgment. In fact, all consciousness supposes a 
judgment, as all consciousness supposes a discrimination.'— ReioVs Works, p. 
242. To the same effect is the following passage from Aquinas (in Perihenn, 
lect. 1) : ' Harum autem operationum prima ordinatur ad secundam ; quia non 
potest esse compositio et divisio nisi simplicium apprehensorum. Secunda vero 
ordinatur ad tertiam : quia videlicet oportet quod ex aliquo vero cognito, cui 
intellectus assentiat, procedatur ad certitudinem accipiendam de aliqaibus 
ignotis.' 



MANUAL OF LOGIC. 



SECTION II. 



SIMPLE APPREHENSION^ 

Simple apprehension is defined to be the mere intellectual 
conception of a thing. b It is of two kinds, viz., incomplex and 
complex. Incomplex apprehension is prior in point of time. 

INCOMPLEX APPREHENSION. 

Incomplex apprehension properly implies simple uncom- 
pounded notions ; but, for the purposes of the logician, it is 
sufficient to consider all apprehensions incomplex which are 
verbally expressed by one word, whether that word repre^ 
sents a simple or compound notion. 

Simple notions or intuitions are obtained immediately by 
the mind, and they cannot be analysed into any elements 

a It may be remarked, that the term simple apprehension is often indiscrimi- 
nately used to denote either the faculty of simple apprehension, or an act of this 
supposed faculty; in other words, the mental power, or the notion acquired by it. 
It may be observed also, that the words perception and conception are also 
frequently used to denote either the act or the object. This ambiguity, against 
which the English language does not provide, is completely obviated by the 
Latin. A perception (perceptio) denotes the mere act of perceiving ; a. percept 
(perceptum) denotes the result of the act. In like manner, a conception 
(conceptio) signifies the mere act of conceiving, while a concept (conceptual) 
signifies the thing conceived. 

Mr Mansell is of opinion, that simple apprehension is synonymous with con- 
ception, in the proper sense of the term. This is true with regard to mediate, 
but not immediate, notions. 

b Nudus rei conceptus intellectivus. — Aldrich. 

Operatio qua mens recipit notiones. Notio est representamen rei in ratel- 
lectu. — Murray's Comp., Part I. 

c Any one word (whether representative of a simple or a compound idea) 
denotes an incomplex simple apprehension in its logical sense. So also any 
number of words, when combined so as to form a sentence, become representa- 
tive of complex apprehension. — Huyshe, p. 2. 

Incomplex apprehension is of one object, or of several without any order or 
reference ; as, a king, a throne. Complex apprehension is of several objects, 
with such order or reference ; as, a king upon a throne. — Jackson, p. 2. 



b MANUAL OF LOGIC. 

more simple than themselves. Compound notions, on the 
other hand, are obtained mediately; that is, they are the 
results of many previous mental states.* 1 

It is by incomplex apprehension, that the mind ac- 
quires the notions represented by each word in a sentence, 
when the words are considered separately. The term ' in- 
complex ' cannot be affirmed of any notion denoted by a com- 
bination of words that have a grammatical relation to each 
other, with the exception of such combinations as, ' a street,' 
' a palace,' &c. 

COMPLEX APPREHENSION. 

Any combination of words grammatically related, but not 
forming a proposition, represents a complex notion ; as, ' a 
member of Parliament/ ' the balance of power,' ' a regiment 
of soldiers.' In contradistinction to incomplex apprehension, 
complex apprehension represents the notions implied by all 
the words of a sentence taken collectively. The notions ac- 
quired, both by incomplex and complex apprehension, are 
expressed by simple terms. 

SIMPLE TERMS. 

A simple term is one or more words, expressing the subject 
of a proposition, or what is affirmed of that subject. The 
subject of a proposition may be expressed by one or more 
words ; as, time, wisdom, a troop of cavalry ; and so also 
may what is affirmed of any subject ; as, invaluable, from on 
high, advancing to battle. If we join these subjects by a copula, 
to what is affirmed of them respectively, we shall have two 
terms in each proposition, and no more, e. g. — 

Time is invaluable. 

Wisdom is from on high. 

A troop of cavalry is advancing to battle. 

a A perception immediate and individual, is an intuition ; the same mediate, 
and by means of a mark common to many things, is a conception. — 8. T. Cole- 
ridge. 



MANUAL OF LOGIC. 7 

A proposition, in which the copula and predicate are sepa- 
rated — as, magna est Veritas — is said to be tertii adjacentis; 
and a proposition, in which the copula and predicate form 
one word — as, aves volant, is said to be secundi adjacentis* 

A simple term, whatever number of words it may contain, 
must not be confounded with a sentence or proposition contain- 
ing Si judgment. In a simple term there is nothing affirmed 
or denied. It is a collection of words grammatically related, 
but not connected by a copula, and may be either the subject 
or predicate of a proposition, but not the whole of a proposi- 
tion, e. g., Burton's Anatomy of Melancholy, is a simple 
term ; but Burton's Anatomy of Melancholy is remarkable 
for learning and research, is a proposition. 

As the correctness of simple acts of judgment, as well as 
of prolonged processes of reasoning, depends on the clearness 
and distinctness of our apprehensions, this head of the ancient 
logic treats of the logical instruments that direct us in appre- 
hending well, and the chief instruments are definition and 
division. Our notions themselves may be obscure, or their 
verbal expression may be indistinct. Hence the error inci- 
dent to apprehension is indistinctness. 

Indistinctness in our apprehensions may arise either from 
the imperfections of our faculties, or from a limited know- 
ledge of the objects of which we form our conceptions. In 
the former case the indistinctness is unavoidable, e. g., Our 
conceptions of the Divine Being, his attributes, heaven and 
angels, and of whatever is only communicated to us by reve- 
lation, must be obscure. In the latter case the indistinctness 
is accidental, and may be remedied by study and observation. 
In all cases, the distinctness or indistinctness of our appre- 
hensions will depend on our acquaintance with the object- 
matter. For without a definite and accurate knowledge of 

a This distinction is recognised by Aristotle, but he does not deem it neces- 
sary that the latter should be resolved into the former. It was among the 
Latin commentators that the distinction first acquired prominence. 



8 MANUAL OF LOGIC. 

the meaning of terms, we cannot reason about them with an 
assurance that they are full and true representatives of the 
things signified. 

The error incident to the faculty of judgment is falsity, and 
arises from asserting the agreement or disagreement of things 
according to the knowledge we possess regarding them, and 
not as they are in themselves. Hence such incorrect judg- 
ments; as, 

The earth is stationary. 

The surface of the earth is a plane. 

Dews fall from the air. 

Moonlight is cold. 

The sun rises from the sea upwards. 

The eye judges of distance and magnitude intuitively. 

Judgment is liable to be misled by the senses, authority, 
example, and the passions. 

The error incident to reasoning is & faulty mode of inferr- 
ing (mendosa collectio.) a If our previous apprehensions are 
indistinct, and our judgments regarding them false, new 
judgments deduced from them cannot fail to be erroneous, e. g., 
Sonesty is the whole of religion ; therefore, I may indulge 
in excess with impunity. Qui sapit pauca loquitur ; pauco 
loquor ; ergo, sapio. It frequently happens, on the other 
hand, that from true premisses a false inference is deduced. b 

The object of logic is to obviate these defects, by pre- 
scribing rules for our guidance alike in investigation and 
inference. 

a Mendosa collectio is remedied by the rules of syllogism and induction ; and 
• here logic not only enables us to perform the operation rightly, but also to test 
the correctness of any given argumentation Mansell, p. 6. 

b The Melitans drew an erroneous conclusion, when they reasoned thus : This 
stranger is about to be hilled by a venomous serpent ; therefore, he is a mur- 
derer pursued by vengeance. Nor was their subsequent inference less erroneous, 
when, in consequence of his shaking off the animal without injury, they said he 
teas a god. 



MANUAL OF LOGIC. 



TERMS. 



A term has been defined to be a vicarious sign of a thing 
or idea used by conventional agreement* 

A term is the sign of a thing when it represents an object 
known by any particular sound, or combination of sounds. 
It is the sign of an idea when it conveys by being uttered the 
same idea to the hearer's mind which the speaker had in his 
own. It is a vicarious sign, because it not only conveys the 
idea of an object, but it also supplies the place of that 
object. b 

Whatever sounds, therefore, are not ex instituto, i. e., rati- 
fied by conventional agreement or mutual consent, cannot be 
considered terms — such as groans, shrieks, exclamations, &c, 
which are suggested by nature. 

Terms are divided into three classes — simple, complex, and 
decomplex. c 

a Signum rei vel conceptus ex instituto vicarium. — Aldrich. The term 
'signum' is somewhat indefinite, for anything may b& made a sign, whether 
vocal or not, by conventional agreement. ' Signum vocale' would remove all 
ambiguity. 

In M. Duval Jouve's Logic, p. 201, language is thus divided, — 
( Absolute — Cries and Gestures. 
\ Conventional — Speech. 

{Absolute — Painting and Sculpture. 
Conventional — Emblems, Telegraphic Signs, Hiero- 
glyphics, Writing. 

b Words are merely arbitrary signs, and they do not naturally possess any 
fitness in their sound or form, as necessary in order that they should express 
the ideas or objects intended. If this were the case, all languages would have 
the same words to express the same ideas, which is not the case ; for the same 
sound conveys different ideas in different languages, and not only in different, 
but in the same language, as is the case with equivocal words. — Iiuyshe, p. 1 . 

c The old logicians called a term a vox simplex, a proposition a vox complexa, 
and an argument a vox decomplexa. For by 'vox' they understood not a 
word, but an expression of thought in language. — Moberly, p. 9. 

a2 



Languages ^ 
are 



10 MANUAL OF LOGIC. 



I. OF SIMPLE TERMS. 



Simple terms are of three kinds, viz., Categorematic, Syn- 
categorematic, and Mixed. 

1. Categorematic Terms are also called simple terms 
(termini simplices) and are such as may be used alone either 
as the subject or predicate of a proposition, as omniscience, or 
constituting together with their adjuncts one simple logical 
term, as, the Queen of England. They must express a 
completed act of apprehension, a but no more. In the propo- 
sition, 

Virtue is its own reward, 
the term virtue by itself constitutes the subject, and the term 
reward, with the adjuncts, its own, constitutes the predicate. 
There are therefore only two simple terms. 

This class of terms consists either of nouns substantive in 
the nominative case, used by themselves, nouns substantive in 
the nominative case with adjuncts, or verbs in the infinitive 
mood — these last being, properly speaking, nouns substantive. 
Nouns in the oblique cases are not simple or categorematic 
terms. 

But although simple or categorematic terms may be used 
alone, either as the subject or predicate of a proposition, they 
may consist of an indefinite number of grammatical words, 
provided the combination expresses a complete act of appre- 
hension. In the following propositions, the subject, copula 
and predicate are laid down in regular order ; the copulas are 
printed in italics, and the grammatical words which express a 
simple complex apprehension, either as subject or predi- 
cate, are united by hyphens : — 

a By simple terms, Aristotle means the ' limits or terms {p^ot) into which 
a proposition is resolved.' These are the noun as subject, and the verb as 
predicate, e. g., avis volat. 



MANUAL OF LOGIC. 11 

The — ways — of — wisdom are ways — of — pleasantness. 

Man — that — is — born — of — a — woman is of — few — 
days — and — full — of — trouble. 

The — single — consideration — of — the — progress — of — a — 
finite — spirit — to — perfection is a . — consideration — suffi- 
cient — to — extinguish — all — envy — in — inferior — natures — 
and — all — contempt — in — superior. 

2. Syncategorematjc* Terms are such as in sense form 
only a part of a subject, or predicate, inasmuch as they only 
imply an incomplete act of apprehension, and consequently 
have not enough of independent meaning for a term. Singly 
they express not a term, but a part of a term. This class 
comprises all adjectives, nouns in the oblique cases, verbs, ad- 
verbs, &c. ; b for these by themselves do not express complete 
acts. of apprehension, as they always stand in a relation to 
some other word, either expressed or understood, e. g., The 
following words — single, some, miserable, this, wonderfully, 
truly, of me, him, John's — must be joined with some other 
words, in order to render the act of apprehension complete. 

Some writers on logic are of opinion, that adjectives may 
by themselves constitute a predicate ; they are, however, 
merely syricategorems, and can only form a part of a predi- 
cate, for they require a substantive either expressed or im- 
plied. In the proposition, 

Fame is precarious, 
the word precarious does not constitute the entire predicate, 
for of itself it is incomplete, and must be supplemented by the 
adjection of thing, either expressed or understood. 

a The terms categorematic and syncategorematic, are not used by Aristotle. 
They originated with the Greek commentators. The latter term is compounded 
of Ci/i/, with, and jtar^yo^sw, to predicate, because it is only with some other 
words that terms of this description can be predicated. 

b There is an exception to this when we are speaking of the terms themselves, 
without relation to any other ; as when we state that large is an adjective, or 
that never is an English word. 



1 2 JXANUAL OP LOGIC. 

This will appear still more evident by converting a propo- 
sition, in which the predicate is expressed by an adjective, 
e. g. Some animals are four-footed. This proposition, 
when simply converted, becomes, some four-footed things are 
animals. Now, without the introduction of the word things, 
or heings, this last proposition would be ungrammatical ; and 
since by conversion is meant the transposition of the extremes 
of a proposition, without any change in the extremes, it is 
obvious that the word things, or beings, must have been im- 
plied in the predicate of the converted proposition.* 

3. Mixed Terms are formed by a combination of the other 
two species. They have been distributed into three classes : 
— 1. A mixed term may be made up of two syncategore- 
raatics, as semper, i. e., omni tempore, always. 2. A mixed 
term may be made up of a categorematic, and a syncategore- 
matic ; as, nemo, i. e., nullus homo, none ; and, 3, a mixed 
term may be made up of a syncategorematic, and the copula 
currit, i. e., est currens, is running} 1 

To this class all grammatical verbs must be referred, as 
they are all resolvable into the copula and the participle, 

ft An adjective, however, is capable of standing by itself, as the predicate of a 
proposition ; as when we say, snow is white ; and occasionally even as the sub- 
ject, for we may say, white is an agreeable colour. The adjective is often said 
to be so used by a grammatical ellipsis : snow is white ; instead of, snow is a 
white object ; white is an agreeable colour, instead of, a white colour, or the 
colour of white, is agreeable. The Greeks and Romans were permitted, by the 
rules of their language, to employ this ellipsis universally in the subject, as well 
as in the predicate, of a proposition. In English this cannot, generally speak- 
ing, be done. We may say, the earth is round ; but we cannot say, round is 
easily moved ; we must say, a round object. This distinction is, however, 
rather grammatical than logical. Since there is no difference of meaning 
between round and a round object, it is only custom which prescribes that on 
any given occasion one shall be used, and not the other. — Mill's Logic, vol. i. 
pp. 29, 30. 

b The division and examples are those of Aldrich. The division is a cross 
one ; the parts not being opposed ; for every mixed word must either be catego- 
rematic or syncategorematic. 



MANUAL OF LOGIC. 13 

e. g., I stand, is equivalent to, I am standing ; or, I am a 
person standing* There is an exception in the case of the 
substantive verb, in the indicative mood and present tense, 
when it simply denotes unqualified existence ; for of itself it 
is not a predicate, but may coalesce with a predicate. Its 
sole use is to connect an attribute with a subject. But where 
existence only is affirmed, it may be both copula and predi- 
cate ; as, Deus est, God is. b 



II. COMPLEX TERMS. 

A Complex Term consists of three simple words, for it ex- 
presses judgment. An act of judgment presupposes two com- 
plete apprehensions, the decision as to the agreement or 
disagreement of which is a judgment; and consequently 
the form of language necessary to express an act of judo-- 
ment must consist of three simple words, which to°-ether 
constitute one complex word. The three simple words 
may, however, be expressed in one ; as, scribo — I am 

writing; abest — he is absent; or in two, as, Ipse adest 

He is present. Hence a complex term may be implied by 
either one or two words, if they are respectively resolvable 
into three. But of the three simple words which form a 
complex term, the two denoting the subject and predicate 

« 

a ' A mixed term is, in the only useful sense of the word, categorematic. It 
belongs to the class of what have been called many-worded names.' — Mill's 
Logic, vol. I., p. 30. 

b The copula is means always exists, but, when used in a proposition, it ex- 
presses an existence modified or limited by the predicate ; when employed alone, 
it expresses absolute existence, i. e., that the subject is among the class of really 
existing things. Upon this variation a well-known fallacy was founded — that 
of arguing that, because ' Ptolemy is dead,' (i. e., only exists to us in the way 
that a dead person can, by a remembered or traditionary notion ;) therefore, 
'Ptolemy is' (i. e., has an actual living existence among other living persons,) 
which is a very different statement. — Outline of the Laws of Thought, p. 179. 



14 MANUAL OF LOGIC. 

may consist, as has been shown above, of a number of 
grammatical words, e. g. — 

The — doctrine — which — places — the — chief — good — in — 
the — pleasures — of — the — body is unworthy — of — a — philo- 
sopher. 

The — dialogues — of — Plato are often — very — lively—re- 
presentations— of — conversations — which — might — take — 
place — at — a — great — university — full — of — rival — professors 
— and — eager — disciples. a 

The — origin — and — sufferance — of — evil, is a — question 
which — has — more -— than — any — other — harassed — meta- 
physical — reasoners — but — especially — theologians — and — 
upon — which — it — is — probable — that — no — very — satis- 
factory — conclusion — will — ever — be — reached — by — the — 
human — faculties — in — our — present — state. b 

As to signification, the subject is always first in a sentence, 
and the predicate last. They are often, however, reversed in 
arrangement, e. g — 

Sweet is the breath of morn. 

Shoreless is the sea of praise. 

In deciding on which is the subject and which the predi- 
cate, in such propositions, the meaning of the context must 
be our guide. 

III. DECOMPLEX TERMS. 

A Decomplex Term expresses an act of reasoning, and 
consists of three complex terms or propositions, having a cer- 
tain relation to each other ; for a completed act of reasoning 
implies two previous judgments, from which a new judgment, 
asserting agreement or disagreement, is inferred. Hence, 
when in regular form, it cannot be expressed in fewer than 

a Mackintosh. b Brougham. 



MANUAL OF LOGIC. 15 

three propositions, e. g., In inferring the immortality of the 
soul from its immateriality, the mental process is as fol- 
lows : — The mind first assents to the judgment, that every- 
thing immaterial is immortal; it then assumes, that the soul 
is immaterial; and, lastly, proceeds to a third judgment, viz., 
that the soul is immortal. It is logically represented thus — 

Whatever is immaterial is immortal. 

The human soul is immaterial ; therefore, 

The human soul is immortal. 
Or in inferring the sphericity of the earth, from its casting a 
circular shadow, the same process is repeated, thus — All 
bodies which, in whatsoever position they may be, cast 
a circular shadow, are spherical. The earth is a body which, 
in whatsoever position it may be, casts a circular shadow ; 
therefore, the earth is spherical. Or in inferring that an 
infant is not responsible, from its not being capable of deli- 
berate crime, thus — 

No being incapable of deliberate crime is responsible. 

An infant is a being incapable of deliberate crime ; therefore, 

An infant is not responsible. 

OF THE LOGICAL TERM. 

The Logical Teem is defined by Aldrich: 'Terminus sim- 
plex sine tempore significativus' a — i. e., a term which is signi- 
ficant, and has no reference to time. This definition is 
obviously inaccurate, for although it excludes reference to 
time, it does not exclude relation; and therefore fails in 
giving the logical term a sufficiently absolute character. By 
excluding relation to time, the logical term becomes opposed 
to the verb. The following definition is more accurate : A 
logical term is a word which is significant, and inexpressive 
of relation or time. This additional limitation excludes all 
adjectives and nouns in the oblique cases from being logical 

a <puvrj (SrtfAavrixri Kara gvv&qxyjv avsv ^govov — Aristotle. 



16 MANUAL OF LOGIC. 

subjects or predicates. By this definition, a logical term is 
equivalent to a simple term, or categorem, and consequently 
excludes adjectives, nouns in the oblique cases, verbs, &c, 
except as forming a part of a subject or predicate ; for as 
these have no complete and independent signification of their 
own, they can merely serve to qualify or denote the relation 
between the words with which they are joined. By Aristotle 
the oblique cases of the noun were named vrooffsig ovoparog, 
i. e., fallings or flexions of the noun, and the past or future 
tenses of the verb were termed vroxsug gr^arog. 

A logical term must not be confounded with a grammatical 
term or phrase. It is employed to express distinctly an idea, 
simple or complex, particular or universal. 

The word or words employed to express a subject or pre- 
dicate, constitute a logical term ; as, 

Wisdom is valuable. 

A clock is a mechanical contrivance, to show the progress 
of time. 

Criminal indulgences are benumbing to the moral feelings. 
Unsought advice is the dictate of presumption. 
All the metals are fusible by heat. 

Logical terms are divided into singular and common. 

A Singular Term expresses the notion formed of an indi- 
vidual object and its qualities. Hence it is called in logic an 
individual noun (individuum & ), borrowing that distinctive 
epithet from the nature of the notion it represents — namely, 
an individual notion, or the apprehension of an individual 
object. Such a notion cannot be divided either by classifi- 
cation or enumeration, for its object is numerically one. 
Anything that has actual existence is singular, i. e., numeri- 

a The accurate etymological sense of the word individuum is plainly that which 
has no qualities which we know of — quod nihil habet dividui — but is an object 
of sensation (perception) known to us only by its occupying a certain space at 
a given time. — Moberly, p. 11. 



MANUAL OF LOGIC. 17 

cally one, and is therefore capable of being expressed by a 
singular sign or term ; as, a sofa, a coach, a tree, &c. 

So long as our knowledge is very contracted, this may be 
done ; but as knowledge becomes increased, it would be bur- 
densome to appropriate a distinct name to each individual 
object. 

But when we merely consider the general nature and cha- 
racter of an object expressed by a singular term, i. e., its 
being of such a description as may equally apply to other 
single objects, the inadequate or incomplete view thus taken 
of it is expressed by a common term, e. g., When we use 
the term bridge, we do not refer to any particular individual 
bridge; but when we say this bridge, we refer to some 
existing bridge, distinguished by accidents or peculiarities 
from all other bridges. It is evident, therefore, that singular 
terms, which denote any one individual object, cannot be 
affirmatively predicated of anything but themselves ; in 
other words, they cannot be the predicate of any affirmative 
proposition, unless its subject be a term expressive of that 
same individual object which the singular term represents, 
e. g., This river, and the Danube, are singular terms, which 
cannot be predicated of anything but themselves; for we may 
say, This river is the Danube, but we cannot predicate of 
any other river that it is the Danube. Singular terms may 
be used, however, as the predicate of any negative proposi- 
tion, whose subject does not express the same individual ob- 
ject, e. g., JEtna is not Mount Blanc. 

All proper names are singular terms; as, England, the 
Thames, Aristotle, fyc. 

Singular terms are sometimes employed (not logically, but 
figuratively) as common nouns ; as, 

The Cicero of his day. 

The grand Napoleon of the realms of rhyme. 

A Common Term is a name which is capable of being 
affirmed truly in the same sense of each of an indefinite num- 



18 MANUAL OF LOGIC. 

ber of individuals. It does not represent anything that has 
actual existence, but an idea or nature common to many indi- 
viduals ; and this common notion is formed by classing 
various objects together that have common points of resem- 
blance. Common terras denote a whole class. A class is 
the indefinite multitude of individuals denoted by a common 
name ; as, bird, flower, conqueror, river, and any individual 
in that class, and, consequently, may be affirmatively predi- 
cated of all or any one of these individuals, e. g., An eagle 
is an individual included in the common term, i bird.' Hence 
we can say, An eagle is a bird; and in the same way, we can 
say that a daisy is a flower, and that the Tweed is a river, 
A common or general name must be distinguished from a 
collective name. A general name is one which can be predi- 
cated of each individual of a multitude ; a collective name 
cannot be predicated of each separately, but only of all taken 
together. 

Common terms are called predicables, from their capability 
of being affirmatively predicated of several things, viz., the 
individuals they denote. 

It ought to be remembered, that a common term does not 
give us an adequate notion of an individual, because in form- 
ing a class (of which a common term is merely the sign or 
expression) we attend to points of resemblance, but exclude 
points of difference. And it is the inadequacy occasioned by 
this exclusion of points of difference or accidents, that renders 
it equally applicable to any of the individuals possessing the 
property or properties which have been abstracted, and which 
are designated by that common term. If, for instance, we 
exclude from consideration all the peculiarities which distin- 
guish l Sicily' from any other island, and merely attend to 
the circumstance of its being surrounded with water, we form 
a notion expressed by the common term island; but this 
notion does not adequately distinguish Sicily, for it does not 
imply any of its peculiarities, and is therefore equally appli- 



MANUAL OP LOGIC. 19 

cable to any one of an indefinite number of islands, or in the 
plural to several together.* 

A Definite Term is one to which the negative particle is 
not prefixed. 

An Indefinite Term 1 * is one to which the negative particle 
is prefixed ; as, that man is not a Swede. The negative par- 
ticle is termed indejinitant, because when prefixed to a noun 
it renders that noun indefinite. In the proposition, That man 
is not a Swede, the term Swede is used indefinitely ; for when 
it is asserted of that certain man that he is not a Swede, the 
class Swede alone is excluded, and to what other class of men 
he may belong remains wholly undefined. 

The definite and indefinite terms together constitute a per- 
fect division or dichotomy. Thus all animals are either 
rational or not rational ; all created things are either 
sentient or not sentient, corporeal or incorporeal. All men 
are either virtuous or not virtuous. 

A Positive Term speaks of a thing as being present, i. e., 
possessed by a subject ; as, a rational man ; a living man ; 
pleasant society ; a man of 'feeling ; a mortalloodj ; el fruit- 
ful vine ; a man of wit ; a man of merit* 

A Privative Term denotes the absence of a thing from a 
subject capable of possessing it ; as, an uneducated man ; un- 
pleasant sounds ; immortal fame ; an unfeeling wretch ; a 

a See Abstraction and Generalisation. 

b Nornen infinitum — Aldrich. More properly, nomen indefinitum — ovofta 
uooitirov. This mistranslation of Boethius has been the cause of error, among 
others, to Kant. — Sir W. Hamilton Relays Works, p. 685. 

c Names which are positive in form are often negative in quality, and others 
are really positive, though their form is negative. The word inconvenient, for 
example, does not express the mere absence of convenience ; it expresses a 
positive attribute — that of being the cause of discomfort or annoyance. So the 
word unpleasant, notwithstanding its negative form, does not connote the mere 
absence of pleasantness, but a less degree of what is signified by the word 
painful, which it is hardly necessary to say is positive. — Mill's Logic, vol. i. 
p. 52. 



20 MANUAL OF LOGIC. 

fruitless search ; an unconstitutional declaration ; the de- 
merit of our works. 

A Negative Term denotes the absence of a thing from a 
subject incapable of possessing it ; as, a lifeless corpse ; un- 
pleasant sarcasms ; the senseless rock ; the unfruitful elm ; 
the demerit of sin. 

An Univocal Teem has one signification only, and in that 
one signification it is equally applied to many things. Thus 
man, genus, electricity, are univocal terms for they always 
signify the same thing. 

An Equivocal Term has more than one signification, and 
in each of its different meanings is a distinct common term — 
the coincidence in sound or sense, or both, being purely acci- 
dental. That some words should be used in different senses, is 
unavoidable, owing to the scantiness of language, e. g., a Club : 
a stick ; a society. Mail: a post-bag; armour. Tract: a 
small book ; an extent of country. Ounce : a species of ani- 
mal ; a legal weight. Palm : a species of tree ; the interior 
of the hand. Page: an attendant; side of a leaf in a book. 
Bull : the animal ; the Pope's official letter ; a blunder. 

Analogous Terms are such as have one meaning, with 
various applications and modifications. In this class of terms 
a few only of the leading ideas are retained, while the 
terms themselves are appropriated in a modified and sub- 
ordinate sense to objects which bear no more than an analogy 
or similarity to their original application. 

A word the same in form and sound, if it be predicated of 
several subjects in the same sense, i. e., to express the same 
collection of qualities, is univocal; if in different senses, i. e., 

a In reality, an equivocal or ambiguous word is not one name, but two names 
accidentally coinciding in sound. File standing for an iron instrument, and^/e 
standing for a line of soldiers, have no more title to be considered one word, 
because written alike, than grease and Greece hiive, because they are pro- 
nounced alike. They are one sound, appropriated to form two different words. 
— Mill's Logic, vol. i. p. 57. 



MANUAL OF LOGIC. 21 

to express different collections of qualities, and these connected, 
is analogous ; if unconnected, equivocal, e. g., Man is predi- 
cated of John and Thomas, univocally ; of Thomas and his 
picture, analogously ; of an island and Thomas, equivocally. 
The following are examples of analogous terms : — 

Sting : of an animal ; of conscience ; of an epigram. 

Judgment : a legal decision ; a faculty and an act of the 
mind. 

Fall : the act of dropping ; moral degradation ; the 
autumn ; diminution in price ; musical cadence. 

A vein of the body ; of metal ; of poetic feeling. 

Heat ; caloric ; the sensation produced by caloric. 

Intention : the state of being strained ; purpose ; close 
attention ; application of a word. 

Justice: social right; punishment; the administrator of 
social right or legal punishment. 

Sacramentum : a military oath ; a christian sacrament. 

In these examples, the resemblance in signification is in 
some cases more, and in others less distinct, though in every 
instance some analogy may be traced. 

A Concrete Term is the name of an object, and represents 
a quality in connection with a subject ; in other words, it ex- 
presses the quality, and at the same time implies the subject 
in which that quality exists ; as, brave, wise. The words 
brave, wise, cannot be used without at the same time imply- 
ing or referring to the beings possessed of the qualities, 
bravery, wisdom; but bravery and wisdom are abstract 
ideas, and might be used without any reference whatever to 
the subjects, brave , wise. Concrete nouns consist of ad- 
jectives, and words which, though substantively used, are 
equivalent to adjectives ; such as, fool, philosopher, astrono- 
mer, geometrician, &c. These are all concretes, of which 
the abstracts are folly, philosophy, astronomy, geometry, 
&c. 



22 MANUAL OF LOGIC. 

An Abstract Term is the name of an attribute, and ex- 
presses a quality by itself, without any reference to the 
subject in which it exists ; as, wickedness, selfishness? 

An Absolute or Non-Relative Term, as opposed to a 
relative term, denotes a word whose meaning is complete in 
itself, and does not imply a relation to any other thing. 

Absolute terms are also named non-connotative, as merely 
denoting an object, without implying any attribute of that 
object ; as, Paris, Romulus. 

A Relative Term expresses an object as related to some 
other, or an idea which cannot be apprehended without 
having at the same time a notion of its correlative. Thus, 
father implies the notion of son, and son of father ; such are 
also king and subject, cause and effect, whole, half, double, 
treble, great, small, swift, slow, high, low. 

Every relative term has its correlative. The correlative is 
that which the relative term suggests. Thus the word 
children calls up the correlative parents. In this case 
children is the relative, and parents the correlative, term. 
The word parents, again, suggests children, in which case the 
word parents is the relative, and children the correlative. In 
short, the same term may be either a relative or a correlative, 
according as it suggests or is suggested. 

Agreeing Terms are such as express qualities which can 

a Do abstract names belong to the class of general, or to that of singular 
names f Some of them are certainly general ; I mean those which are 
names not of one single and definite attribute, but of a class of attributes. 
Such is the word colour, which is a name common to whiteness, redness, &c. 
Such is the word magnitude, in respect of the various degrees of magnitude and 
the various dimensions of space ; the word weight, in respect of the various de- 
grees of weight. Such also is the word attribute itself, the common name of 
all particular attributes, ut when only one attribute, neither variable in 
degree nor in kind, is designated by the name ; as, visibleness, tangibleness, 
equality, &c, then the name can hardly be considered general ; for though it 
denotes an attribute of many different objects, the attribute itself is always con- 
ceived as one, not many. — Mill's Logic, vol. i. pp. 35, 36. 



MANUAL OF LOGIC. 23 

be affirmed of any one object at the same time; as, a theory 
may be popular and dangerous; an edifice may be massy 
and elegant. Agreeing terms are sometimes called compati- 
ble or consistent terms. 

Opposite Terms express qualities which cannot be affirmed 
of any one object at the same time, e. g., A style cannot be 
said to be eloquent and bald at the same time ; neither can 
we say that a report can be at once true and false, nor a 
man miserable and happy. At different times, however, 
opposite terms may be predicated of the same object. Thus, 
a man may be said to be active to-day, and inactive to- 
morrow. 

Terms of Primary and Secondary Intention.* 

A first or primary intention is properly defined a concep- 
tion of a thing or things formed by the mind from materials 
existing without itself; as, man, animal, tree, A second 
intention is a conception of another conception or conceptions, 
formed by the mind from materials existing in itself; as, 
genus, species, accident, &c. 

'Notions are of two kinds; they have either regard to 
things as they are — as, horse, ship, tree, and are called first 
notions — or to things as they are understood, as notions of 
genus, species, attribute, subject, and in this respect are called 
second notions, which, however, are based upon the first, and 
cannot be conceived without them. Now logic is not so much 
employed upon first notions of things as upon second ; that 
is, it is not so much occupied with things as they exist in 
nature, but with the way in which the mind conceives them. 
A logician has nothing to do with ascertaining whether a 
horse or a ship or a tree exists, but whether one of these 
things can be regarded as a genus or species, whether it can 
be called a subject or an attribute, whether from the conjunc- 
tion of many second notions a proposition, a definition, or 

* This distinction is of Arabian origin. 



24 MANUAL OF LOGIC. 

a syllogism can be formed. The first intention of e very- 
word is its real meaning; the second intention its logical 
value, according to the function of thought to which it 
belongs.' a 

Connotative Terms. All concrete common terms are 
connotative. They denote a subject, and imply an attribute. 
The common term man, for example, denotes Cicero, Quin- 
tilian, Juvenal, &c, and any other number of individuals, 
because it is the name of the class to which, as a class, they 
belong ; and it is applied to them not only in virtue of their 
possessing, but as denoting that they do possess certain 
marks or attributes. 

There is another class of terms, which, although individual 
terms, are called connotative : e. g., ' the author of the Iliad' 
connotes (i. e., notes along with it) ' Homer ; ' ' the founder 
of Rome ' connotes ' Romulus ;' 'the capital of France ' con- 
notes i Paris.' b 

a Outline of the Laws of Thought ; pp. 39, 40. 

A first notion is the conception of a thing as it exists of itself; as, John, 
man, animal. A second notion is the conception not of an object, as it is in 
reality, but of the mode under which it is conceived by the mind itself; as, 
individual, species, genus. The former is the conception of a thing — real, im- 
mediate, direct ; the latter the conception of a conception — formal, mediate, 
reflex. — Sir W. Hamilton, Ed. Rev. vol. lvii. p. 210. 

Whately and a host of others define the first intention of a term to be a cer- 
tain vague and general signification, and the second intention to be the more 
precise and limited, which it bears in some particular art, science, or system. 
This misconception, which is to some extent countenanced by Aldrich, has 
arisen from confounding the words intention and meaning. Intentio — 
svratiig — in this application properly signifies a stretching of the mind to a 
thing. The examples usually given are of analogous terms, not of terms of the 
first and second intention. 

b In treating of terms, no particular method has here been followed. The 
proper division is into singular and common, as it is exhaustive of the whole 
class. With the exception of the terms distinctively designated singular, all 
the terms above explained are really common terms employed in different ways, 
and named accordingly. 



MANUAL OF LOGIC. 25 

CHAPTER II. 
SECTION I. 

ABSTRACTION AND GENERALISATION. 

A correct understanding of the processes indicated by these 
terras respectively, will be of advantage in studying the doc- 
trine of the predicables. 

1. Abstraction. — Abstraction literally signifies a drawing 
off, or taking away from; but in its strict and secondary sense 
it means the separate consideration of one or more of the 
parts or qualities of any species of whole, omitting or exclud- 
ing for the moment all consideration of the other co-existing 
qualities. This process invariably precedes generalisation. 
The parts or qualities excluded at one time may again be 
made the objects of new abstractions, and become the ground- 
work of new classes denoted by common names. 

When, therefore, we draw off and consider separately any 
part or quality of an object a presented to us, we are said to 
abstract ; and with this simple act the province of abstraction 
terminates. * 

We may, for example, attend to the fragrance of a violet, 

a There is a prevalent confusion regarding the meaning of the words subject 
and object. ' Not to understand these words,' remarks the author of the ' Out- 
line of the Laws of Thought,' note, p. 52, ' is a disqualification for the study of 
modern philosophy. The subject is the person who receives impressions ; the 
object is the external thing which gives them. When I see a mountain, I am 
the subject, and the mountain the object. Subjective, therefore, would mean 
" relating to the mind that thinks;" objective "relating to the thing thought 
of." This use of the words, though now universally followed, is of modern 
origin ; formerly that in which any qualities inhered was called the " subject" 
of them, a very different use of the word.' — [For a masterly disquisition on 
this point, see Tappan's Elements of Logic, sect, iv.] 

B 



26 MANUAL OF LOGIC. 

and for the moment exclude all consideration of its form and 
colour, or we may contemplate its form and colour, disregard- 
ing its fragrance ; and in either case, after this individual 
violet (which may have been the first we have ever seen) is 
withdrawn from our consideration, we still retain a notion 
of its fragrance, or notions of its form and colour; and the 
notions thus retained are properly termed conceptions. 

Again, a person may have for the first time seen a sheep, 
and may have attended to, or abstracted the circumstance of 
its having four legs, excluding from consideration all the 
other co-existing marks ; and the conception remaining in 
the mind, after this individual was no longer present, wculd 
be that of a four-footed animal. If he had heard the name 
sheep applied while contemplating it, this name, when uttered 
again in his hearing, would also suggest the conception of a 
four-footed animal, and, in the circumstances, this would be 
properly termed a reproduced notion. 

By abstraction, then, the mind fastens upon a particular 
quality or mark, and separates it from the co-existing aggre- 
gate of qualities. Hence when abstracting, we think of the 
properties or marks, and not of the object to which they 
belong. 

Instances might be multiplied indefinitely, but those given 
above will suffice to show the exact nature of what is termed 
abstraction, and that it should not be confounded, as it too 
frequently is, in logical treatises, with its co-process generali- 
sation. 

2. Generalisation. — We have seen that, in abstracting, the 
mind attends to the consideration of any one or more of the 
qualities or parts, of any species of real or ideal whole, disre- 
garding for the moment all the remaining co-existing parts or 
qualities, and that beyond this its province does not extend. 
It is manifest, however, that if we could not classify the 
abstracted attributes or marks according to some relation 
subsisting between them, our knowledge would be of little 



MANUAL OF LOGIC. 27 

practical advantage. But the difficulty of making our know- 
ledge available is obviated by a natural tendency in the mind 
to proceed from abstraction to generalisation ; in other words, 
to assemble together and classify all such qualities or parts of 
wholes as possess common points of resemblance or agree- 
ment ; and when any two or more of these are classed toge- 
ther, we are said to generalise, and we express the generalised 
property or mark by a common or general term. 8. It is not to 
be supposed, however, that what is implied by a common 
term has any actual existence. We conceive it to exist, 
merely for the purposes of classification and generalisation. 

Common or general terms are always employed as signs of 
general notions, and are obtained by comparing several indi- 
vidual objects with each other ; and after noting the marks or 
points in which they agree, as well as several in which they 
differ, we lay aside the consideration of the latter, and adopt 
and class all and only those points in which the individual ob- 
jects appear to agree with each other. A common term is 

a We cannot generalise without having first abstracted ; but whether there 
may be abstraction without generalisation is a question not quite agreed upon. 
In the ' Lessons on Seasoning,' (usually attributed to Archbishop Whateley) 
the following passage occurs: — ' The two words have not the same meaning ; 
for though we cannot "generalise" without "abstracting," we may perform 
abstraction without generalisation. If, for instance, one is thinking of " the 
sttn" without having any notion that there is more than one such body in the 
universe, he may consider it without any reference to its place in the sky, whe- 
ther rising or setting, or in any other situation (though it must be always 
actually to some situation); or, again, he may be considering its heat alone, 
without thinking of its light, or of its light alone, or of its apparent magnitude, 
without any reference to its light or heat. Now in each of these cases there 
would be abstraction, though there would be no generalisation, as long as he 
would be contemplating only a single individual — that which we call the "sun." 
But if he came to the belief that each of the fixed stars is a body affording 
light and heat of itself, as our sun does, he might then, by abstracting this 
common circumstance, apply to all and each of these (the sun of our system, 
and the stars) one common term denoting that circumstance — calling them all 
"suns." And this would be to generalise.'' 



28 MANUAL OF LOGIC. 

consequently only applicable to the several objects in respect 
of that which is common to them all, and therefore makes 
no account of the differences between them. In this way 
we obtain a term denoting the individuals themselves, in 
respect of their points of resemblance, and this we designate 
a concrete common term ; or we obtain a term implying the 
points or circumstances in which the various individuals 
agree, which we call an abstract common term, e. g., From 
noting the various points of agreement in various individual 
kings, we obtain the common term king, while the term 
■royalty, which is an abstract common term, denotes the 
qualities or properties common to them all. And so also in 
the case of any other common term. 

In order to generalise, it is not necessary that there should 
be an exact resemblance between the objects denoted by a 
common term. Similarity in certain points is sufficient. 
Accidents, and non-essential attributes, are not taken into 
account. If accidents and subordinate properties were re- 
garded, generalisation would be impossible, because no two 
objects are in every respect alike. It is by omitting minor 
points of difference that we proceed from individuals to 
species, and from species to general 

Generalisation must, in the first instance, be from indivi- 
duals to species ; and in illustration of the process, we may 
take Socrates, Aristotle, Plato, Kant, Leibnitz, Male- 
branclie, &c. Now by excluding from consideration the 
various circumstances in which they differ from each other, 
and attending to the attribute predicable of them in com- 
mon, we form the general notion denoted by the common 
term, philosopher. In like manner, from Hesiod, Homer, 
Pindar, Sophocles, JEschylus, Virgil, Horace, Juvenal, &c, 

a In early life our generalisations are involuntary ; they are in a manner 
forced upon us by the recurrence of individual objects possessing the same 
marks ; but when we begin to form classes for the purposes of arrangement 
and knowledge, we generalise intentionally. 



MANUAL OF LOGIC. 29 

we derive the common name, poet ; from Herodotus, Thucy- 
dides, Livy, Tacitus, &c., the common name, historian; from 
Demosthenes, Cicero, Hortensius, &c, the common name, 
orator. This is the simplest form of generalising, viz., noting 
one common point of agreement.* 

But we may generalise by noting in several individuals a 
plurality of points of agreement. If, for instance, we observe 
a variety of objects, and each provided with a mast, a sail, and 
a rudder, as common points of resemblance, and if we attend 
to these only, we form the notion expressed by the common 
term ship ; and this generalised notion is applicable in the 
same sense to every individual ship contained under the class 
ship, since each of them possesses marks corresponding to 
the component parts of this common notion, as none have 
been taken into account except those implied by the term 



It is obvious, however, that each of the individuals denoted 
by this common term has certain peculiar attributes which 
the others have not, and which, entering into the comprehen- 
sion of some particular individual, must confine the applica- 
tion of the peculiar attributes to some one particular ship. 
Hence the notion of any individual ship is more complex 
than that expressed by the common term ; for in forming it, 
the distinctive marks peculiar to each were excluded from 
consideration. 

a We are enabled not only to separate and consider singly one part of an object 
presented to the mind, but also to fix arbitrarily upon whatever part we please, 
according as may suit the purpose we happen to have in view, e. g., any indivi- 
dual person to whom we may direct our attention niay be considered either in a 
political point of view, and accordingly referred to the class of merchant, farmer, 
lawyer, &c, as the case may be; or, physiologically, as negro or white man; 
or, theologically, as Pagan, Mahometan, Christian, &c. And so, in respect of 
anything else that may be the subject of our reasoning, we arbitrarily fix upon 
and abstract that point which is essential to the purpose in hand ; so that the 
same object may be referred to various different classes, according to the occa- 
sion. — Whateley's El, book I., sect. vi. 



30 MANUAL OP LOGIC. 

But generalisation is not only from individuals to species. 
We may apply abstraction to the common terms denoting 
species, and ascend to a class still higher. The words dog, 
sheep, con; lion, horse, each denote a common notion obtained 
by abstraction and generalisation, from the individuals of 
which they are respectively predicable ; and as in these we 
discover attributes common to all of them, we may resume 
the former process, and divest these classes of their respective 
formal characteristics, and express the notion comprehending 
all the marks in which they resemble each other by the com- 
mon term, quadruped. Generalisation may evidently be 
carried to almost any extent by considering common nouns 
(for instance, quadruped) as singular; for by omitting their 
points of difference, we arrive at new aggregates, expressed by 
more general terms. Thus from quadruped we may arrive 
at the more general term, animal, and from animal we may 
obtain the still more general term, corporeal being. By pro- 
ceeding in this way, laying aside points of difference, and 
considering only points of resemblance, we arrive ultimately 
at substance or being, the highest possible generalisation. 

It will be seen from the foregoing, that abstraction is in a 
certain sense analytic in its character ; for by it we separate 
mentally all the attributes and marks of a whole. Generalisa- 
tion is, on the other hand, synthetic in its nature ; for by it 
we collect into classes all such attributes or marks of wholes as 
have common points of resemblance or agreement. 

It is not requisite that the individuals from which we 
obtain a common or general notion should co- exist. Suc- 
cession in point of time is sufficient, e. g., We could have 
the common notion Icing, if only one had existed at a given 
time, in the same manner as we have the common notion 
Pope, which is founded on the points of agreement noted in a 
succession of individual Popes. We can reason about either 
of them without necessarily referring to any one individual 
king or Pope. 



MANUAL OF LOGIC. 31 

The process of abstraction, and the use of common terms, 
are subordinate to that arrangement and classification, with- 
out which our knowledge could not be applied to much prac- 
tical use. The elements of our knowledge are almost unli- 
mited, both in number and variety; and on this account 
classification becomes an unavoidable necessity. After we 
have abstracted and generalised accurately, we can make the 
results the objects of separate examination. We may, for 
instance, contemplate at pleasure, number, form, weight, 
colour, motion, attraction, heat, electricity, &c. ; and the 
results are related to some of the most important sciences 
with which mankind are conversant. 

It follows that the only limit to our power of forming 
classes is the capability of tracing differences upon which to 
ground distinctions; and the only rule that requires to be 
observed, is to make the classification subservient to our con- 
venience, whether for the purpose of recording or examin- 
ing/ 

Common terms expressive of a class are nouns substantive; 
as, field, flower, city, rock, tower, desert, &c. ; but points of 
difference, whether essential or accidental, are denoted by ad- 
jectives, and the use of the adjective is to limit the meaning 
of the noun to certain individuals. Of themselves, adjectives 
have no independent meaning ; they merely indicate or connote 
attributes, whetner of objects, of attributes, or of feelings. 
By means of adjectives, instead of requiring a separate noun 
substantive for each object to be denoted, one noun-substan- 
tive, coupled with appropriate adjectives, will serve to denote 
many objects. Thus we say, tall man, short man, amiable 
man, active man, useful man, &c. So of colours, we call 
them bright, dark, pleasing, gloomy, vivid, lively, &c. ; and 

a It is the employment of the power of generalising that constitutes the cha- 
racteristic distinction between the higher and the lower animals. The highest 
form of instinct can neither form nor comprehend a general notion. It cannot 
go beyond the knowledge of an individual and its accidents. 



32 MANUAL OF LOGIC. 

of characters, we say they are just, cruel, decided, vacillating, 
sagacious, reflecting, &c. ; and of affections, we say they are 
intense, moderate, absorbing, divided, lasting. 

It may not be out of place to refer here briefly to the 
furious controversy which long existed between the sects of 
Eealists and Nominalists, regarding the nature of Universals, 
and which only terminated when a more important question 
— the Reformation — diverted their attention from it. Por- 
phyry, in his treatise on the predicables, probably originated 
the strife by the following passage : — ' Whether,' he says, 
6 genus or species are substances, or exist in bare thought 
alone, or, supposing them to be substances, whether they are 
material or immaterial, and, again, whether they exist sepa- 
rately or in composition with sensible objects, I must decline 
discussing. The subject is profound, and needs a separate 
and more detailed inquiry.' 

Averroes may be regarded as the founder of the Realists, 
although his view of the matter was but a species of neo- 
Platonism. He held that genus and species were substances, 
but left it matter of doubt whether these substances existed 
apart from matter, or whether they were to be considered as 
always present in the concrete.* Among the schoolmen, long 

a Reid states the Platonic doctrine of ideas summarily as follows: — ' Plato 
and his masters held that there are objects of intellect of a superior order and 
nature which are permanent and immutable. These are ideas, or universal 
natives, of which the objects of sense are only the images and shadows. To 
these ideas they ascribed the most magnificent attributes. Of man, of a rose, 
of a circle, and of every species of things, they believed that there is one idea or 
form, which existed from eternity, before any individual of the species was 
formed ; that the idea is the exemplar or pattern, according to which the Deity 
formed the individual species ; that every individual of the species participates 
of this idea, which constitutes its essence. Thus the idea of every species, 
though one and immutable, might be considered in their different views or 
respects— first, as having an eternal existence before there was any individual 
species ; secondly, as existing in every individual of that species without division 
or multiplication, and making the essence of the species ; and, thirdly, as an 
object of intellect and science in man. — Int. Powers, essay 5, cap. 6. 



MANUAL OF LOGIC, 33 

before Nominalism took its rise, this doctrine was generally 
considered heterodox. They acquiesced in it only in conceiv- 
ing the Universal to be an actual existence. They held that 
genera and species were really existing things — that they 
existed actually as substances, and not merely as conceptions 
of the mind — that there was an universal man existing as one 
and the same in Socrates and Plato, and all the individuals of 
the species — and that the various individuals are formed by 
the addition of accidents to the species. 

Roscelin of Compeigne founded the sect of the Nominalists. 
He held that universals were nothing but names. Roscelin 
was followed by Abelard, who held an intermediate view 
between absolute nominalism and realism. He believed 
universals to be conceptions, but without an independent and 
objective reality. In order, however, that these conceptions 
should be formed and retained in the mind, they must rest on 
the signs of language ; but he made conceptions turn on the 
proposition, while Roscelin made them tarn on the simple 
term. His doctrine, however, continued vague and assailable 
until the days of Occam, whose opinions correspond with that 
of modern conceptualists. a He held that genera and species 
existed, but existed only in the mind — that every universal is 
really a singular in itself, and therefore is only a universal in 
virtue of its signification, which is a sign of many things. 5 
The following is a specimen of his reasoning : — ' If the realist 
opinion,' he remarks, ' were true, God could not anni- 
hilate one individual without destroying all ; for to annihilate 
one individual, he must destroy all that is of its essence. 
Consequently, he must destroy the universal which exists 
both in it and in other individuals ; and these could not con- 
tinue to exist when deprived of a part of their substance, such 
as the universal is supposed to be.' 



a Aristotle has been claimed as a realist, a conceptualist, and a nominalist. 

b Nullum universale est aliqua substantia extra animam esistens, Occam, 

b2 



34 MANUAL OF LOGIC. 



SECTION II. 

EXTENSION AND COMPREHENSION. 

The extension of a term means the number of individual 
things of which severally that term may be predicated ; in 
other words, it regards the number of species into which a 
genus, or the number of individuals into which a species may 
be divided. Thus of the term flower the parts of extension 
are violet, lily, blue-bell, daisy, buttercup, &c, because of all 
these and of as many more as answer to the description, the 
term flower may be predicated. For as we have seen, com- 
mon terms denote a whole class, and any individual in that 
class; and may therefore be predicated of all or any one of 
these individuals. 

The parts of extension of a genus are consequently the 
species contained under it, and of a species the individuals 
contained under it. 

The comprehension — otherwise called the intension — of a 
term means all the simple notions which, taken together, 
make up the more complex notion signified by the term; 
in other words, it is the aggregate of all the known properties 
of a genus, species, or individual, to which it may be applied. 
Thus the notions of substance, body, life, sensation, and 
reason, are the parts of comprehension of the term man. 

By keeping in view what is meant by the extension, and 
what by the comprehension of a term, it will be seen that a 
singular term has the least extension of all ; for it can only 
be predicated of the one individual thing to which it belongs, 
while, on the contrary, a singular term has a greater compre- 
hension than a term denoting a class, i. e., a common term. 

Of common terms some have a wider and some a more 
restricted extension, according to the number of things to 
which they may be applied in the same sense. Common 



MANUAL OF LOGIC. 35 

terms denote an aggregate of singulars classed together, 
and the extension of a terra will therefore depend on the 
amount of generality which an attribute or mark possesses, 
or the number of individuals to which it belongs. Thus the 
common term man has a greater extension than the common 
term city, as it can be predicated of a greater number of 
individuals; the term city, again, has a greater extension 
than the term university, and tree than river, and so on. 
The extension, therefore, or, as it may be termed, the quantity 
of a term, is the number of individuals contained under it, 
and of all or any one of which it may be predicated in the 
same sense. 

By making terms the objects of reflection, we shall dis- 
cover that some involve a smaller and others a greater num- 
ber of ideas ; in other words, that some are less and others 
more complex, according to the number of component parts of 
which they consist, e. g., The notion expressed by the term 
flower is less complex than that expressed by the term violet 
— for this reason, that the term violet implies all the ideas or 
component parts of the term flower, and, in addition, all the 
notions which distinguish that particular species of flower 
from all others. 

It follows that the aggregate of simple notions, which make 
up the more complex notion expressed by a term, consti- 
tutes what is called its comprehension ; and also, that differ- 
ent terms have a greater or smaller comprehension, in pro- 
portion to the degree of complexity they imply. This may 
easily be seen, by analysing or resolving a term into its com- 
ponent ideas or parts. 

The terms instanced in, viz., flower and violet, may be 
viewed, then, under two different aspects — 1st, With regard 
to the number of individuals of which they may be predi- 
cated ; and, 2d, with regard to the complexity of the notions 
which they imply, or, in other words, with regard to their 
extension and comprehension. 



36 MANUAL OF LOGIC. 

On considering these terms closely, we discover that the 
term which has the greater extension has the smaller com- 
prehension, and vice versa. The notion expressed by the 
term violet is more complex, or consists of a greater number 
of simple notions, than the complex notion expressed by the 
term flo rver, and the individuals of which the term violet may 
be affirmed, or which may be termed violets, are fewer in 
number than the individuals which may be termed flowers. 

For in addition to the notion of an individual of the flower 
tribe, the term violet is intended to express the notions of a 
particular form,, colour, and fragrance which some flowers 
have, and which some have not; and as these notions of 
form, colour, and fragrance are contained in the comprehen- 
sion of the term violet, that name can only be affirmed of such 
flowers as have that particular form, colour, and fragrance. 

It follows from this, that each component notion, in the 
comprehension of a term, limits the application of such term 
to those things which have a corresponding character ; and, 
therefore, that the greater the comprehension of a term, the 
smaller is the number of individual objects to which it may 
be applied, or the less is its extension. 

The comprehension of a term denotes its extension. Sup- 
posing that we know the term rhinoceros to denote an ani- 
mal, and that we wish to ascertain what other animals may 
be called by that name, we must, in the first place, learn the 
exact meaning of the term, i. e., we must become acquainted 
with all the less complex notions, which, when taken together, 
form the more complex notion expressed by that term ; and 
when we have ascertained all these, and see some other 
animal which does not possess corresponding attributes, we 
affirm immediately that this animal is not a rhinoceros, or 
that this individual animal is not included in the extension of 
the term rhinoceros, since the term can only be applied to 
such animals as possess attributes corresponding to the com- 
plex notion expressed by that word. 



MANUAL OF LOGIC. 37 

It frequently happens, that the comprehension of one term 
is included in the comprehension of another, e. g., The com- 
prehension of the term flower is included in that of the term 
violet ; for all the component notions that make up the term 
flower are implied also in the term violet, but it has its own 
peculiar attributes besides. In this case the extension of the 
latter must be included in the extension of the former ; for 
since the notion of a flower includes in it no attributes that 
are not also contained in the notion of a violet, every indivi- 
dual that may be named a violet must possess all the attributes 
which the comprehension of the term flower includes, and 
may be therefore also named a flower, or is contained in the 
extension] of the word flower. 

Since the comprehension of a term determines its exten- 
sion, it is manifest, that if the comprehension of any two 
terms be identical, their extension must also be identical, and 
that if the extension of any two terms be the same, so in like 
manner must be their comprehension. 

It will easily be seen from the foregoing, that a singular 
term has, of all terms, the smallest extension, as it consists of 
only one individual, while its comprehension, on the other 
hand, must be greater than that of any common term ; for 
peculiar attributes enter into its comprehension which cannot 
enter into that of any common term. 

In the highest genus the comprehension is necessarily the 
least, and the extension greatest, while in the lowest species 
the comprehension is greatest and the extension least. 



38 



MANUAL OF LOGIC. 



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MANUAL OF LOGIC. 39 

t 

SECTION III. 

OF THE PREDICABLES.* 

The processes of abstraction and generalisation, as has been 
already observed, are subordinate to that classified arrange- 
ment of conceptions which renders our absolute knowledge 
practically advantageous. But, amidst the mass of general 
notions acquired, the mind discovers certain distinguishing 
qualities-, which may form the basis of a new and complete 
arrangement of them under certain distinct heads. Many 
outlines for such a classification have been suggested, but that 
which has been generally adopted is the fivefold division into 
genus (yss/o;), differentia (d tup op a), species (s/<5og), proiprium 
(tdiov), and accidens (<rv{j.(3e&ri%o$). These are named the five 
predicables or universals. h 

The term predicable has been defined 'nomen commune 
univocwm secundce intentionis 9 or a common univocal noun 
of the second intension. It is univocal, because, although 
applicable to many individuals, it is considered as representa- 
tive of only one idea ; and it is of the second intention, as 
being the conception of a conception. 

The object of the doctrine of the predicables is to reduce 
to certain classes all conceivable predicates, or whatever can 
be logically asserted about any subject. 

a The five heads of Predicables, or five-fold division of general names, were 
■written by Porphyry, in the third century, as an addition to the Aristotelian 
Logic. They are contained in his Isagoge or Introduction to the Categories of 
Aristotle. That Aldrich's views differ considerably in many points from those 
of Porphyry, will be seen from the notes in the sequel. 

b Aristotle's enumeration of the predicables differs considerably from that of 
Porphyry. The former only mentions genus (ysvogj, property (tdtov^, definition 
(ofOs)j and accident (tfu/x/3s/3>j%oj.) Differentia has no distinct place as- 
signed to it, but is considered as belonging naturally to the genus (wg ovffotv 
yzvizrjv.') Species is regarded as constituted not so much by the combined 
notions of the genus and difference as from the marks of two concurrent or com- 
municant genera. 



40 MANUAL OF LOGIC. 

There are five distinct classes of relations which may ob- 
tain between a subject and a predicate, for of any subject we 
may affirm its genus, or its differentia, or its species, or its 
proprium, or its accidens. 

In conceiving of some imaginary common nature — as, 
man, triangle — we are naturally led to conceive, also, that 
this supposed essence or nature is composed of parts, and 
that the conception of it may therefofte be resolved into more 
simple conceptions ; for instance, the conception of man 
resolves itself into those of animality and rationality ; tri- 
angle into figure, and the quality of having three sides. These, 
again, suggest other conceptions as belonging to the primary 
essence or nature ; as, risibility, nobility to man; the having 
three angles; the being equilateral to triangle. 

These in their order we term the essence, the part of the 
essence, and the quality joined to the essence. The essence 
consists of two parts, of which one is common to it, and to 
other essences, as animality is common to man and brute, 
figure to triangle, circle, square, &c. The other is peculiar 
to the essence, and distinguishes it from all others, and forms 
it that which it is, i. e., rationality distinguishes man from 
all other animals ; the having three sides distinguishes tin- 
angle from all other figures. 

But the quality joined to the essence may be twofold, 
as being either necessarily or contingently united with it. 
Thus with man the idea of risibility is necessarily joined, 
while the ideas of nobility, tallness, &c, are only contingently 
joined. With triangle, the having three angles is necessarily, 
but the being equilateral, or isosceles, &c, is only accidentally 
joined. 

These have been termed, as above stated, the five predic- 
ates or universals. It may be proper to remark, however, 
that the predicable and the universal are not one and the 
same. The former is the sign expressive of the latter. The 
predicable is that which is asserted of many, and the univer- 



MANUAL OF LOGIC. 



41 



sal is one nature existing in many, or the ens unum in 
multis. 

The subjoined examples may be of use to the student : — 



Genus, 


animal. 


Differentia, 


rational. 


Species, . 


man. 


Propriuni, 


possessing speech. 


Accidens, 


learned, illiterate, &c. 


Genus, 


juice. 


Differentia, 


extracted from grapes. 


Species, . 


wine. 


Propriuni, 


inebriating. 


Accidens, 


sweet. 


Genus, 


sentence. 


Differentia, 


declaratory. 


Species, . 


proposition. 


Proprium, 


true or false. 


Accidens, 


categorical, modal, &c. 


Genus, 


substance. 


Differentia, 


having solid extension. 


Species, . 


body. 


Propriuni, 


occupying space. 


Accidens, 


white, red, &c. 


Genus, . 


water. 


Differentia, 


falling from the clouds in drops 


Species, . 


rain. 


Proprium, 


fertilising the earth. 


Accidens, 


cold, violent, excessive, &c. 


Genus, 


surface. 


Differentia, 


bounded by one or more lines. 


Species, . 


figure. 


Proprium, 


enclosing space. 


Accidens, 


large, small, &c. 



42 



MANUAL OF LOGIC. 



Genus, 


' . figure. 


Differentia, 


having three sides. 


Species, . 


triangle. 


Proprium, 


having three angles. 


Accidens, 


equilateral, isosceles, &c. 


Genus, 


star. 


Differentia, 


wandering. 


Species, . 


planet. 


Proprium, 


describing an elliptical orbit- 


Accidens, 


seen from the earth. 


Genus, . 


institution. 


Differentia, 


possessing the highest executive 




power in a country. 


Species, . 


government. 


Proprium, 


able to enact or abrogate laws. 


Accidens, 


monarchial, despotic, &c. 



The above examples have been selected - on account of 
their simplicity, and with the view of showing that all the 
more important knowledge we possess, regarding the nature 
of a thing, may be briefly summed up by the five predicables. 
When we say, ' Man is a rational animal, possessing speech, 
learned,' &c, we give an adequate account of his nature. 
The object of all investigations into the nature of things, is to 
ascertain all the predicables that bear relation to them ; and 
our knowledge must always be confined to the predications 
we can make with certainty. It is a simple matter to refer a 
species to its true genus. We readily refer iron to the genus 
metal ; eagle to the genus bird, &c. ; but to decide on the 
individual quality which essentially 'distinguishes one species 
from another, and what specific property is to be held as 
flowing necessarily from the essential attribute of any given 
species, is often a point of extreme difficulty. Even in the 
examples prefixed, simple as they are, many of the differentiae 
and propria are by no means beyond the reach of objection. 



MANUAL OF LOGIC. 



43 



SCHEME OF THE PORPHYRIAS TREE. 



Substance. 



Divisive. 

Corporeal. 

Constitutive. 

Divisive. 
Animate. 

Constitutive. 



Body. 



Divisive. 

Incorporeal. 



Divisive. 

Inanimate. 



Living Body. 



Divisive. 

Sensitive. 

Constitutive. 
Divisive. 

Rational. 

Constitutive. 



Animal. 



Divisive. 

Insensitive. 



Divisive. 

Irrational. 



Man. 



►tf 


o 


> 


H- 


o 


CO 


3 


o 

H 


2 


fc 


Q 


s 


3 


H 


a 

CO 


i 



W 9 M 



DO 

O 



A 



44 MANUAL OF LOGIC. 

In this simple scheme of the Porphyrian Tree, substance is 
taken as the highest genus, and man as the lowest or infima 
species; all the other terms in the direct line between sub- 
stance and man are subaltern terms. The scheme may be 
thus explained : — Substance, taken as the highest genus, is 
divided, as indicated by the term ' divisive,' into two species 
— ' corporeal,' and ' incorporeal.' On the left side are the 
logical differentia, which distinguish each species from the 
collateral species belonging to the genus immediately above it. 
On the right side are the differences of those collateral species 
which are not specified in the scheme. ' Substance,' then, as 
has been said, is divided into ' corporeal' and ' incorporeal ;' 
by combining the terms 'corporeal' and 'substance,' i. e., 
the differentia and genus, they constitute, as indicated by the 
term ' constitutive/ the species ' body,' which is one and the 
same with corporeal substance. Then, again, considering 
' body' as a genus, it is divided into ' animate' and ' inani- 
mate;' and, by combining 'animate' and 'body,' we consti- 
tute the species ' living body.' Living body may, however, 
be considered a genus, and as such may be divided into 
'sensitive' and 'insensitive,' and, by combining 'sensitive' 
and ' living body,' we constitute the species ' animal.' Ani- 
mal may also be considered a genus, and is divisible into 
' rational' and ' irrational,' and, by uniting ' rational' and 
animal,' we constitute the species ' man,' which is equivalent 
to rational animal. ' Man,' however, is an infima species, 
and is consequently only divisible into the individuals con- 
tained under it. 

The term genus denotes the material, or common part of 
an essence ; differentia, the distinguishing or formal part of 
an essence; species, the whole of an essence; proprium, some 
property necessarily joined to an essence ; and accidens, some 
property contingently joined to an essence. 

The predicables belonging to each of these five classes are 
predicated or asserted in the same sense of many things, 



MANUAL OF LOGIC. 45 

namely, of all those objects in which the common or universal 
nature represented by the term is supposed to exist. 
First. We can predicate of any subject its genus ; as, 

Violets are flowers. 
Daisies are flowers. 

Here the term flowers denotes the genus, and is predicated of 
both violets and daisies, two of the species comprehended 
under it. Or, secondly, its species ; as, 

This plain figure is a triangle. 
This plain figure is a square. 

Here the terms triangle and square denote species, and are 
predicated of their genus plain figure. Or, thirdly, its differ- 
entia, i. e., the formal and distinguishing part of its essence ; 

as, 

A triangle is a figure contained by three sides. 

Here, contained by three sides, denotes the differentia, and is 
affirmed of triangle , of which alone it is predicable. Or, 
fourthly, its proprium ; as, 

Every triangle has three angles — 

the property of having three angles being necessarily joined 
to the differentia, contained by three sides. Or, fifthly, its 
accidens, i. e., something accidental to it — a quality which is 
found in some, but not in others ; as, 

This triangle is equilateral. 
Men are wits. 
Bodies are round. 

Here the terms equilateral, wits, round, are accidents to the 
subjects triangle, men, bodies. 

It must be kept in view, however, that each of these heads 



46 MANUAL OF LOGIC. 

of predicables is a relative term ; for that which is a genus, 
when predicated of some things, may be a differentia, species, 
proprium, or accidens, when predicated of other things. 3 In 
short, we cannot say what predicable any term is, or whether 
it is really one, until it be specified of what it is to be predi- 
cated, e. g., The term sound is a genus, in relation to the 
species contained under it, viz., sharp sound, flat sound, &c. 
On the other hand, it is the differentia of a sounding body, 
the proprium of bodies, which, from their nature, are capable 
of producing sound, and it is an accident of bodies in 
general. b 

definition and explanation of the five predicables. 

1. Of Genus. 

Genus is defined to be a universal predicable, predicated in 
' quid ' of many things differing in species, as the material or 
common part of their essence. 

Things are said to differ in species, or, specifically, when 
viewed as divided into different classes. 

Terms which belong to the class genus express common 
natures, derived not immediately from the comparison of 
individuals, but from the comparison of several classes or 

a Although in their application the predicables are to be viewed as relative 
terms, yet, when regarded as the species contained under a genus, their relation 
to each other is determinate and opposed. 

b It is to be remarked of these distinctions, that they express not what the 
predicate is in its own meaning, but what relation it bears to the subject of 
which it happens on the particular occasion to be predicated. There are not 
some names which are exclusively genera, and others which are exclusively 
species, or differentiae, ; but the same term is referred to one or another predic- 
able, according to the subject of which it is predicated on the particular occa- 
sion. Animal, for instance, is a genus, with respect to man or John ; a 
species, with respect to substance or being. The words genus, species, &c. are 
therefore relative terms ; they are names applied to certain predicates, to ex- 
press the relation between them and some given subject. — Mitt's Logic, p. 162. 



MANUAL OF LOGIC. 47 

species already formed by abstraction and generalisation from 
individuals; and it is for this reason that such terms are 
technically said to be predicated of things differing in species. 
The term genus denotes a class that has immediately under 
it two or more classes or species, and each of these, if not 
species infima, must have at least two other species or classes 
under them. It is an universal term, and the classes under it 
must be universal terms, *. e., they must be expressive of 
species or classes. Thus the genus 

Animal 

comprehends under it the classes man, beast, bird, fish, insect, 
which are also all universal terms. A term, therefore, which 
only includes singulars under it cannot be a genus. 

Genus, then., is an abridged expression of all the collected 
properties found in the subject species, with the exception of 
the differentice, and the properties resulting from them. 

There are two kinds of genus, viz., summum and subalter- 
num. The summum, or highest genus, is the last step in 
generalisation. Any genus that cannot be considered a spe- 
cies of anything, is a summum genus. A summum genus 
can therefore in no case be a species, as it manifestly can 
have no constitutive differentia. 

Summum genus, in its strictest signification, is that all- 
extensive term under which every object of whatever kind 
may be classed, and of every one of which it may be affirma- 
tively predicated. The w r ord generally used to express it is 
substance, or, as some call it, being. It is the highest and 
most general notion which the mind can conceive, and cannot 
consequently be classed under any superior genus. Many 
other genera are, however, frequently used as summa genera, 
according as they may be most suitable for any particular 
science or system. Thus by an ornithologist, bird would be 
regarded as the summum genus under which he w T ould class 
the various subdivisions of birds ; in like manner, fish would 



48 MANUAL OF LOGIC. 

be regarded as the sumraum genus most applicable to the 
study of ichthyology. 

Any term between a highest genus and a lowest species, 
expresses a species with reference to the genus above it, but 
a genus with regard to the species below it ; and such terms 
are respectively named genus subalternum, and species sub- 
alterna. This will be more clearly illustrated by an ex- 
ample : — 

Highest Genus. Lowest Speciei. 

Substance, Body, Living Body, Animal, Man. 

Here body is a species with reference to its genus substance, 
but a genus with reference to living body, which is one of the 
species included under it. Living body, again, is a species 
with reference to its genus body, but a genus with reference 
to animal, which is one of its subject species. Animal, on 
the other hand, is a species with reference to living body, but 
a genus with reference to man, being one of the species which 
it comprises. Man is the lowest species (species infima), in- 
cluding under it no terms except the proper names of individual 
men, and cannot therefore be considered a genus of anything. 
Species still lower might be formed, indeed, if we were to 
classify men according to their country ; as, American, 
Asiatic, African, European, or, according to their size, age, 
or colour; but such classifications would proceed on acciden- 
tal, not on essential distinctions. 

In the series substance, body, living body, animal, man, the 
term substance is the highest genus, and cannot be a species 
of anything more abstract, as it is the last step in generalisa- 
tion ; and the term man is the lowest species, and cannot be 
considered a genus, as it is the first step in generalisation. 
With the exception, therefore, of the terms substance and 
man, every other term in the series is a genus subalternum 
with regard to the term below it, and a species subalterna 
with regard to the term above it. 



MANUAL OF LOGIC. 49 

In any series of this kind, it is evident that the summum 
genus has the least comprehension and greatest extension of 
all the terms, being the name of the simplest conception, and 
that the species infima has the greatest comprehension and 
the least extension of them all, although, as a universal term, 
it has a smaller comprehension, (as it excludes accidents) and 
greater extension than any of the singular terms included 
under it. 

Genus, as already mentioned, means the material or com- 
mon part of an essence ; a and hence it can only be predicated 
of things differing in species. "When we say violets are 
flower 's 9 daisies are flowers, the affirmation is only made as to 
the common part of their essence, i. e., their common points of 
resemblance. Violets and daisies, and all other flowers, pos- 
sess certain qualities in common, and it is upon these that the 
genus is founded. The characteristic and distinguishing attri- 
butes do not enter into the comprehension of the genus. But 
every attribute included in the comprehension of the genus 
is predicable of every one of its subject species. 

It follows that a genus can only express an essence inade- 
quately, since it merely expresses a nature common to many 
things, excluding from its comprehension all the distinguish- 
ing characteristics of the species of which it may be predicated. 

A genus is called & logical or universal whole, because it 
is the most extensive term in its signification, containing 

a From what has been said at the close of the last section, regarding realism 
and nominalism, it will readily be seen that the definitions here given of the 
predicables' are strictly realistic in their character, for they cannot be defended 
except on realist principles ; that is, that genera and species are not mere con- 
ceptions of the mind, but have an independent existence in nature. Like most 
of the scholastic definitions, they are simple, clear, and terse, and not likely to 
be replaced by anything preferable. Indeed, all definitions of the subjective, as 
the predicables are now universally regarded, are characterised by less or more 
looseness and vagueness ; at all events, they fall short -of the exactness and pre- 
cision which can be secured in definitions of the objective. The definitions are 
those of Aldrich, who probably took them immediately from Albertus Magnus. 

C 



50 .MANUAL OF LOGIC. 

species as its subject parts, and affirmatively predicable of all 
of them, as may be seen from the following example, viz. : — 
'Men \ 



All 



Beasts 

Birds 

Fishes 

Jnsects 



C 

are Animals. 



Here animal is the logical whole, and men, beasts, birds, 
&c, its contained parts. 

A logical whole — such as a genus — has only parts of ex- 
tension, while a metaphysical, or essential whole — such as 
a species — has parts of comprehension. 

Genus is said to be predicated in ' quid' (sv ry n s<rn). If 
in reference to a genus the question tre asked, Quid est 
Mud f the answer is, The common or material part of the 
essence of many things differing in species. Strictly speaking, 
however, we cannot answer the question, Quid est ? for we 
do not know of anything Quid sit, what is its essence ; and 
can only say Quale sit, i. e., we know it only indirectly 
through its attributes and marks. 

The species into which a genus is divided are termed co- 
ordinate or cognate species. They are termed 'co-ordinate/ 
as not being subordinate to one another, and 'cognate,' as pos- 
sessing certain marks or conceptions in common. The genus 
of which co-ordinate or cognate species are sub-divisions, is 
termed the proximate genus to them all, while in this case 
the summum genus is called the remote genus. All the other 
genera, between it and the proximate genus, are called inter- 
mediate genera. 

II. Op Species. 

Species is a predicable predicated in ' quid,' of many 
things differing in number, as the whole of their essence. 



MANUAL OF LOGIC. 51 

Things are said to differ in number, or numerically, when 
viewed as divided into individuals. The numerical difference 
is constituted by the peculiar accidents, which distinguish the 
individuals contained under an infima species from one an- 
other. 

Terms which belong to the class species represent the 
general or common notion of some nature conceived to exjst 
in a number of different individuals ; and it is for this reason 
that a species is technically said to be predicated of things 
differing in number. 

A species, then, is an abridged expression of the collective 
marks of the individuals contained under it, with the ex- 
ception of their accidents. Thus city is a species, including 
Athens, Rome, Carthage, Paris, London, Oxford, &c. 
River includes the individuals — the Tyber, the Scamander, 
the JSalys, the Danube, the Thames, Isis, Cam, &c. Man 
denotes a species, comprehending Socrates, Plato, Aristotle, 
Anacreon, Homer, Virgil, Thucydides, Herodotus,Tacitus, 
&c. Star, includes the Polar Star, Arcturus, Bootes, Sirius, 
&c. 

A species is denoted by a universal term. It is any class 
included under a higher class, which must be its genus* We 
say any class, because a genus has generally many classes 
under it, and in any case must at least have two. 

Species is of two kinds, viz., species subalterna, and species 
infima. The latter expresses the first common nature, 
founded on the observation of similar marks in a number 
of individuals. It is the first step in generalisation. A 
species infima cannot be considered as a genus with respect to 
anything, as it only contains individuals under it. a Thus the 

a An infima species could be considered a genus, if we were at liberty to 
raise accidental differences to the rank of essential differences. On this sup- 
position, we might divide man (an infima species) into learned and uniearned, 
churchman, dissenter, priest, layman, or into white, black, or red man. On 
this point Mr Mill remarks, vol. i. p. 164:— 'By the Aristotelian logicians, 



52 MANUAL OF LOGIC, 

universal term mastiff is a species infima, including under it 
only individual mastiffs. In contradistinction to a species 
subalterna, a species infima is termed species proper, that 
is, the species of logic. 

The attributes by which the individuals contained under a 
species infima are distinguished from each other, are acciden- 
tal, e. g., it is accidental to a man to belong to a particular 
country ; to be an astronomer, or botanist, &c. ; but the attri- 
butes by which the different species of the same genus are 
distinguished from one another, are essential. 

A species denotes the whole of an essence ; for it is made 
up by the union of the genus and differentia. These are the 
component parts of a species ; for the genus denotes the com- 
mon or material part, and the differentia the formal, or cha- 
racteristic part. Thus by uniting the two parts, a plane 
figure (the genus), and contained by three sides (the differ- 
entia), we form triangle, which is a species of figure. 

A species can have but one differentia. This attribute is 
peculiar to it, and distinguishes it from every other species of 
the same genus ; but although a species can have only one 
differentia, it may have many propria, or subordinate attri- 
butes, resulting from or accompanying that differentia. 

It is obvious that the differentia cannot be included in 
the comprehension of the genus ; for if it could, it would be 
common to all the species ; neither can any of the attributes 
resulting from the differentia enter into the comprehension of 
the genus. 

the terms genus and species were used in a more restricted sense. They did not 
admit every class which could be divided into other classes to be a genus, or 
every class which could be included in a larger class to be a species. Biped 
would not have been admitted to be a genus with reference to man, but apro- 
prium or accidens only. It was requisite, according to their theory, that 
genus and species should be of the essence of the subject. Animal was of the 
essence of man ; biped was not. And in every classification they considered 
some one class as the lowest infima spscies.' 



MANUAL OF LOGIC. 53 

Species, like genus, is said to be predicated in { quid ;' but 
species is predicated as to the whole of the essence of many- 
things differing in number, whereas genus is merely predi- 
cated of the material or common part of the essence of many 
things differing in species. 

It must be borne in mind, when we speak of species as 
expressing the whole essence, that no predicate can com- 
pletely and strictly express the whole essence of its subject, 
unless it be another word of the very same import and co- 
extensive with it; as, Wellington was the conqueror of 
Napoleon. The words whole essence must therefore be un- 
derstood as meaning only the whole that any common term 
can express, i. e., the nearest approach to the whole essence 
of the individual that any term not synonymous with the 
subject can denote. 

When species is spoken of as a whole, this is properly in 
reference to the genus and differentia, each of which denotes 
a part of that species which is constituted by the union of 
both. a 

Species being the whole essence, as explained above, 
necessarily implies the genus, which is a part of that essence. 
It is a more complete and comprehensive term than genus, 
and is therefore a metaphysical, or essential whole, e. g., 
Man is a metaphysical whole, and implies rational ani- 
mal. 

a The author of the ' Outline of the Laws of Thought,' in examining Aris- 
totle's view of the predicable classes, explains species thus : ' The species may 
be regarded as composed not of the marks of the genus and difference, so well 
as of those of two concurrent or communicant genera ; for the difference is but a 
genus which, from its overlapping part of another, is used as a distinctive mark 
of that part which it overlaps. If in analysing our notion of " the red flower- 
ing currant," we regard " currant " as the genus, and " red flowering " as the 
difference, we may also regard " red flowering " as a wide genus, wider, in 
fact, than " currant ;" and therefore we may say, that our notion of the plant 
is generated by the concurrence of two genera.' — [P. 148; see also p. 39, 
supra. - ] 



54 



MANUAL OF LOGIC. 



The 


following scheme 


exemplifies subaltern genera and 


infima species : — 


' Vulture, 




/Rapacious, ■ 


Falcon, 
, Owl, &c. 
' Parrot, 




Pies, ■< 


Hornbill, 






, Crow, &c. 
( Turkey, 




^Land Birds,... / 


Gallinaceous, - 


Pheasant, 
^ Partridge, &c. 






Columbine, 


Pigeon, &c. 
' Thrush, 






Passerine, - 


Finch, 


Birds, ) 




, Lark, &c. 






VStruthious, ■ 


Dodo, 
Ostrich, &c. 






r Cloven-footed, 


r Heron, 
Snipe, &c. 




V Water Birds, .. ( 


Pinnate-footed,...- 


■ Phalarope, 
. Grebe, &c. 






Web-footed, - 


' Duck, 
Diver, &c. 



MANUAL OF LOGIC. 55 



DIFFERENTIA. 

Differentia* is a predicable, predicated in ' quale quid,'' 
(sv ru voiov ri) of many things differing either in species 
or in number, as the distinguishing part of their essence. 

It has been already shown that things are said to differ in 
species, or specifically, when viewed as divided into different 
classes, and to differ in number, or numerically, when viewed 
only as individuals. 

The differentia is the formal or distinguishing part of an 
essence, and is variously termed the essential difference or 
attribute, the divisive and constitutive part, and, in common 
discourse, the characteristic part. It must be positive, not 
negative. 

A differentia belongs to a species alone, and every species 
included under a genus must have a differentia peculiar and 
belonging to itself, exclusively, in order to distinguish it from 
every other species of the same genus. Thus under the 
genus plane figure we have the species triangle, square, 
circle, oblong, &c, each of which has its own formal or 
distinguishing part, in addition to the common or material 
part plane figure, e. g., the being contained by three sides is 
the essential difference of a triangle, for it constitutes the dis- 
tinction between it and all other figures, since no figure can 
be a triangle which is not contained by three sides, nor can 
any three-sided figure be anything but a triangle. 

The differentia first divides the genus, and then constitutes 
the species. Thus the genus animal is divided into two dis- 
tinct species, by adding the attribute rational to one part of it, 

a Porphyry recognises only a relative difference between two given species. 
Thus rationale is not the differentia of man per se, but of man as distinguished 
from brutes. Hence he defines man ^a>ov "koyi/iov dvrjrov (a rational mortal 
being) — the last term being in like manner the differentia of man, as compared 
with the gods. — Mansell, p. 21. 



56 MANUAL OF LOGIC. 

and the attribute irrational to another part of it, e. g., 
rational animal, or man ; irrational animal, or beast. 

"With respect to its dividing the genus, it has been termed 
divisive (differentia divisiva); and with respect to its con- 
stituting the species, it has been termed constitutive (differ- 
entia constitutiva). a 

It is by the differentia that the various species contained 
under a genus become opposed to each other, and such oppo- 
sition consists in each species having some one essential 
attribute peculiar to itself alone. In short, it signifies the 
attribute which distinguishes a given species from every other 
species of the same genus. 

Porphyry gives five definitions, or, rather, explanations of 
the differentia, but they are all substantially one ; for the same 
differentia is either formal, or divisive, or constitutive, &c, 
according to the view in which it is for the time regarded. 

The differentia is predicated in quale quid, e. g., to the 
question, What is a man? with reference to his genus, the 
answer is an animal, but to the question Quale animal ? what 
description of animal, with reference to his species, the answer 
is rational. The answer to 'quid' points out the material 
part, and the answer to ' quale,' the distinguishing part, and 
both taken together complete the species or whole essence. 

GENERIC AND SPECIFIC DIFFERENCE. 

There are two kinds of difference, viz., generic and spe- 
cific. 

Generic difference is that which constitutes subaltern 
species. It is termed generic, because the species which it 
constitutes may be considered as a subaltern genus, and con- 



a Hasc divisio est ejusdem rei in diversos tantum modos ; eadem enim dif- 
ferentia perpetuo est et divisiva et constitutiva, diverso tamen respectu.— San- 
derson. 



MANUAL OF LOGIC* 57 

sequently the generic difference may be affirmatively predi- 
cated of every species which is contained under it ; and hence 
it is predicated of things differing from each other in species, 
e. g., sensitive may be predicated of beast, bird, Jish, insect, 
as well as of man, for it is a generic difference to all animals. 
Specific* difference is that which constitutes infima species. 
It is this kind of difference which is distinctively meant by the 
logical difference. It can be predicated of all the individuals 
contained under the species which it constitutes, and is there- 
fore said to be predicated of things differing in number. Thus 
rational, which is the specific difference of man, is predicable 
of every man, but not of any other animal. 

proprium. 

A proprium is a predicable, predicated in 'quale ' of things 
differing either in species or in number, as necessarily joined 
to their essence. 

Terms which belong to the heads differentia, proprium, 
and accidens, are said to be predicated of things differing 
either in species or in number, because they may have imme- 
diate reference either to a genus, in which case they are pre- 
dicated of all the species contained under that genus, or to a 
species, in which case they are predicated of the individuals 
from which that species is formed. 

A proprium is a quality necessarily joined to an essence, 
but not its differentia. It is predicated universally and ex- 
clusively of all the individuals of a species, but is predicable 

* Specified (differentia) est quag speciem infimam constituit; haec est, quae de 
numero differentibus predicatur. — Aldrich. This differs somewhat from the view 
of Porphyry, who considers the specific difference (hicMpo^a sibortoiog) as opposed 
to accidental difference, (<5/a<£>oga xara tfu,a/3s/3?j;>co£) — the former denoting 
the differentia proper (i. e., either constitutive or divisive) which distinguishes 
one species from another, whether subaltern or infima — the latter denoting the 
accidents which distinguish between individuals. 

c 2 



58 MANUAL OF LOGIC. 

of no other species. A property of this description forma 
part of the essence of a species, and is the result of the diffe- 
rentia, e. g., the differentia of a triangle is, that it is ' contained 
by three sides ;* and we cannot conceive of a figure contained 
by three sides but as having also three angles. The property, 
therefore, < having three angles,' is the result of the differentia 
1 contained by three sides.' Responsibility r , again, is a pro- 
perty of man, and is the result of the differentia rational. It 
is evident, however, that when we call anything a proprium, 
we should first know the differentia from which it flows, 
because a proprium must be considered as an accident, unless 
deduced from a known differentia. 

A proprium might therefore be defined as the expression of 
those attributes which are observed uniformly to accompany 
a class, though not taken into consideration when forming it. 

GENERIC AND SPECIFIC PROPERTY. 

Property is divided into two kinds — generic and specific. 

Generic property is that which necessarily accompanies or 
is joined to the essence of the summum or subaltern genus. 8 
It is evident from this that generic properties may be predi- 
cated of many species, and of all the individuals contained 
under them, while specific properties can only be predicated 
of the different individuals contained under one species, e. g., 
the property in triangles that ' the three angles are equal to- 
gether to two right angles ' is a generic property, and may 
be predicated of all triangles. 

a Genericum est, quod necessario comitatur essentiam generis summi vel sub- 
alterni. — Aldrich. 

On the principles of Aristotle and Porphyry, a generic property can only be 
regarded as a property with respect to the highest species of which it is predi- 
cate. As regards all subordinate species, it must be considered as an accident. 
Mobile, for example, a property of corpus, is an accident to animal and to homo, 
as not convertible with them. — Mansell, p. 28. 



MANUAL OF LOGIC. 59 

Specific property is that which flows from the essence of 
the species infima, a and is predicated of one species and its 
different individuals, e. g., the property that 'all equilateral 
triangles are also equi-angular,' is a specific property, and can 
only be predicated of that species of triangle which is termed 
'. equilateral.' Generic property is predicable, then, not only 
of species, but also of the various individuals contained under 
those species. Specific property is only predicable of the 
individuals contained under one species. b 

Proprium has also been divided into four kinds : — 

1. That which is peculiar to one species, but not univer- 
sally found in its contained individuals. Thus it is proper to 
man alone to be a physician or statesman, though all men are 
not so. 

2. That which is predicable of the whole species, but not 
of that species alone, i. e., found in every individual of a 
species, but found also in other species. Thus malleability, 

a Specificum. quod Suit ab essentia speciei infimae. — A Idrich. This view of 
property is not countenanced either by Aristotle or Porphyry. Instead of consi- 
dering it as flowing or resulting necessarily from the essence, they regard it as 
simply convertible with its subject. Aldrich's view is, however, a very old 
one, and is probably traceable to the Arabians. 

b The difference and specific property are often difficult to distinguish from 
each other ; but it should be remembered that a property is only joined to an 
essence, and results from the difference; whereas the difference is a con- 
stituting part of the essence. If, then, any part of an essence be supposed 
to be taken away, that essence can no longer remain as it was. The following 
test, therefore, will in most cases succeed : — Since the genus and difference 
united form the species, it follows that if the difference be supposed to be taken 
away from any species, that species must revert to its subaltern genus — in fact, 
the species will no longer exist ; but if a property be supposed to be taken from 
it, the essence, i. e., the species, will not thereby be injured. — Huyshe. In illus- 
tration of this, let us take the following example : — From the species ' rational 
animal' suppose 'rational' to be taken away, and the species immediately reverts 
to its subaltern genus ' animal ' —but suppose, again, the property ' speech- 
possessing' to be taken away, the species ' rational animal' would not thereby 
be destroyed. 



60 MANUAL OF LOGIC. 

fusibility, weight, value, are predicable of gold, but not of 
gold only. 

3. That which may be predicated of all the individuals of 
a species, and of that species only, but not always. Thus, 
vines bear grapes ; man is a laughing animal. 

4. That which may be predicated universally, peculiarly, 
and at all times, of one species only and its individuals. Thus 
it is the property of every circle, and of circles only, that the 
lines drawn from the centre to the circumference are all 
equal. a 

Of these four classes the first is only an accident of the 
species, and cannot therefore be strictly termed a property. 
Every property must be applicable to all the individuals of 
the species, and must belong to that species necessarily, as 
flowing from the difFerentia. A property differs from an acci- 
dent in this, that it can be predicated of its species, and 
vice versa. They are reciprocally predicable, e. g., man u a 
being subject to law. A being subject to law is a man. The 
two propositions are simply convertible. An accident and 
its species are not, however, reciprocally predicable. We can 
assert that every statesman is a man, but we cannot say 
that every man is a statesman, because the being a states- 
man is only predicable of some men, and consequently not 
universally found in the members of the species. 

The second is the generic property. It is characteristic of 

a Quod convenit soli sed non omni, ut homini esse grcmmaticum. 
Quod convenit omni sed non soli, ut homini esse bipedem. 
Quod convenit omni et soli sed non semper, ut homini canescere. 
Quod convenit omni soli et semper ut homini risibiliias. — Aldrich. 

On the above examples Mansell remarks (p. 28) : ' The ibtov of Porphyry 
answers to the fourth kind of property mentioned in the text. The other three 
are accidents, the first and third separable, the second inseparable, . but still 
only an accident, as being predicable of more subjects than homo. On the 
scholastic theory, it is also an accident, as not flowing necessarily from rationale, 
the differentia.' 



MANUAL OF LOGIC. 61 

a genus, and predicable of the different species under it, but 
it is not characteristic of a species as such. 

The third is not sufficiently distinct from the first to require 
separate notice. 

The fourth is the specific property, and is that alone which 
constitutes the proprium of logic. 

ACCIDENS. 

Accidens is a predicable predicated in * Quale ' of many 
things differing in species or in number, as contingently 
joined to their essence , 

An accident denotes something contingently joined to an 
essence, e. g., the being 'equilateral' or 'right-angled' is 
an accident to a triangle, for such attributes do not neces- 
sarily belong to a triangle, since every accident must be sepa- 
rable from the species, otherwise it would be a property. 

Accidens is divided into two kinds — inseparable and sepa- 
rable. 

The inseparable accidents are such as cannot be separated 
from the individuals of which they are predicated. They 
are circumstances which have happened in past time to some 
members of a species, and cannot now be separated from 
them, e. g., the place of birth, the parents, the past events of 
life, &c, are inseparable accidents to any individual man. 
The circumstance or fact of having been born at Mantua, has 
no conceivable relation to Virgil as one of the species man, 
but, as an individual, the circumstance is inseparable from 
him. This class of accidents may be predicated of their 
subjects at all times. 

The separable accidents are such as can be separated from 
the individual, e. g., a man's dress, posture, residence, opi- 
nions, &c, are separable accidents. This class of accidents 
can only be predicated of their subjects at certain times. 

An inseparable accident is predicable only of individuals ; 



62 MANUAL OF LOGIC. 

for all accidents are separable from the genus and species ; 
but with regard to individuals, they are separable or insepa- 
rable. 

The last three heads of predicables, viz., differentia, pro- 
prium, and accidens, are predicated of things differing as well 
in number as in species, because they have a relation either 
to a genus or a species. If they relate to a genus, they can 
be predicated of all the species which that genus contains ; 
and if they have reference to a species, they can be predi- 
cated of all the various individuals under that species. 

In conducting classification on a great scale, as in natural 
history, the technical designations furnished by the predicables 
are found to be too few. Others have therefore been invented 
chiefly to express the varieties of intermediate genera. Those 
best known are used in the Linnsean system, and consist of 
five kinds — 1. Classes, corresponding to summa genera; 2. 
Orders, corresponding to intermediate genera; 3. Genera, 
confined to the proximate genera ; 4. Species, confined to the 
co-ordinate species under each genus ; 5. Varieties, including 
the species infima, and all divisions depending merely on 
accidental, or on some of the less important proper qualities. 
Other systems employ a still greater variety of designations, 
e. g., divisions, classes, orders, tribes, families, legions, sec- 
tions, sub-divisions, &c. 



MANUAL OF LOGIC. 



63 



SO 
P 




< 




ffl 




a 


1 


a 


no 


H 


fc 


>H 


O 


r-l 


rf> 


1— 1 




M 


t> 




Q 


p 

02 


no 


no 


M 


1 




r/7 


H 


W 




tf 




ew 




a 




3 




H 




B 




O 




02 





^ q3 

« a 



H 

o P 
OS 



GO 

s 

9 



© 



© 



"° 9, 
o o 

O id 



CD 

V o 

1 



fc 



n3 




o 2 


f Separable. 


•r-S C 








/13 3 *i 






a c3 




12 o 


^ Inseparable. 


o 




<1 




tT 






f Specific. 


v^& ■< 




OS & 




5Q • 

o o 


\ Generic. 



f Infima. 



Subalterna. 



a.tf 


Specific. 


-a § 






y, Generic. 


-»^r 


- 




C Subalternum 


e material 
or genus. 


k Summum. 



64 MANUAL OF LOGIC. 

SECTION IV. 

OF THE CATEGORIES OR PREDICAMENTS.* 

The five predicables or universals, as has been shown, do 
not express any actually existing thing; they are merely 
terms expressive of common notions, and present them as 
classified under certain distinct heads. They express second, 
not first notions. In nature we find no actually existing 
thing corresponding to genus, species, or any of the other 
predicables. They indicate conceptions^ not realities. 

Second notions, however, presuppose first notions, and as 
under the predicables we classify conceptions, so under the 
categories we classify realities, or distribute into classes all 
the possible real things about which we can discourse. 

In short, a perfect list of categories or predicaments would 
be a classification of whatever can be the subject or predicate 
of a proposition,* while the predicables are a classification of 
all the possible affirmations about these things. 

The usual distribution of the categories, according to the 
Aristotelian school, is into ten ; and it is supposed that to 
some one or other of these heads of division' any term ex- 
pressing a first notion may be referred. The division is as 
follows, viz. : — c 

Ovtia . . . substantia . . . substance. 
Tlotov . . . quantitas . . . quantity. 

a They are termed categories from the Greek noun substantive xarTjyo^a, 
and predicaments from the Latin rendering, predicamentum. The categories 
are said to have been first classified by Archytas of Tarentum ; but of this there 
is no certain evidence. 

b In this the categories of Aristotle are defective ; for many things that form 
the subject and predicate of a proposition are excluded in the enumeration, 
such as entia rationis (beings of the reason) and second notions. 

c The Pythagorean, Platonic, and Stoic schools among the Greeks, had each 
a favourite enumeration of categories. 



MANUAL OF LOGIC. 



65 



Uoiov 


. qualitas . 


. quality. 


TLpog ti . 


. relatio . . , 


. relation. 


nov . . 


. ubi . . . 


. where. 


Uore 


. quando » . 


. when. 


Kg/tf^a/ . . 


. situs . . . . 


« . posture. 


^X SIV 


. habitus . . 


. . habit. 


TLoistv . 


. actio . . 


» . action. 


Ila^s/v 


. passio 


► . suffering. 



To some one of these heads we may refer every term, 
according as may best suit our purpose, for the subject under 
discussion. 

Substance* (answering to the question, ' Quid estf ) consi- 
dered without reference to inhering qualities, has been de- 
fined quod sub se stat, i. e., which supports itself, or which, in 
the mode of its existence, is independent of everything else. 
With reference to inhering qualities, it has been defined 
ens per se subsistens et substans accidentibus, i. e., an entity 
having independent existence and supporting qualities. The 
substance is the ens, the self-existing thing ; the accidens is 
the ens entis, which may be freely rendered the mode, quality, 
or accident of the self-existing entity. 

Substance is divided into first and second substances. In- 
dividual things are first substances; as, Socrates, Buce- 
phalus, this castle, that tree; second substances are denoted 



1 The words substance, entity, being, are each of them less or more ambiguous 
in their signification. Of substance, in its philosophical sense, we have no 
direct knowledge ; we only know it indirectly or through attributes, but when 
in a familiar language we use the word substance, we are supposed to mean by 
it some really existing object or thing cognizable by the senses. Entity and 
being are in their strict meaning synonymous, being both immediately con- 
nected with a verb which simply denotes mere existence. ' Being' is, however, 
commonly used as a synonym for substance, with this difference, that being is 
applied equally to mind and matter, while substance rather suggests the idea of 
matter only. Being and entity should be understood as implying mere abstract 
existence, and never separate existence, as cognizable by the senses. 



66 MANUAL OF LOGIC. 

by common or general terms, which merely denote creations 
of the mind ; as, man, animal, body. This category includes 
whatever constitutes the very being of things, and of which 
all objects of thought are modifications ; substances are 
divided into self-existent and dependent, material and imma- 
terial, &c. 

Quantity. — The answers to the questions, How great? 
How many ? How long in time? &c, fall under this category.' 
It includes all things capable of being measured or numbered. 
Quantity is divided into continuous and discrete. Continuous 
quantity is that whose parts are united by some common 
boundary, such as magnitude, or the modifications of exten- 
sion, having permanent continuity; and time and motion 
having successive continuity. Discrete quantity is that whose 
parts have no continuity, such as number, to which sound and 
speech are sometimes added. 

Quality, (answering to the question ' Quale ?') includes the 
properties which principally distinguish or characterise objects. 
It is divided into natural or innate powers and properties, as 
the mental faculties and the capabilities of objects ; acquire- 
ments, such as learning, virtue ; sensible qualities, such as 
sounds and colours, and forms or figures, with all their modi- 
fications. 

Relation includes all the circumstances about objects which 
imply a connection with others, in considering which we may 
observe both the principle of the relations, and the things 
related, called correlatives, e. g., the consideration of master 
implies servant, and of pastor, flock, &c. 

Place (answering to the question Ubi ?) includes all the 
modifications of space, and the more general relations of 
objects to space. 

Time (answering to the question Quando ?) as to-morrow, 
yesterday, in the year of the building of Rome ; but time im- 
plied by the question quando, must not be confounded with 
the time denoted by the question quam diu ; the latter is 



MANUAL OF LOGIC. 67 

continuous time; as, a month, a year, and belongs to the 
second category. 

Posture includes chiefly the relations of objects to one an- 
other as occupying space, such as the relations of the con- 
stituent parts of objects, the relations of parts to the whole, 
and the relations of entire objects to one another in their 
attributes, combinations, &c. 

Habit expresses what anything has ; as, to be clothed, to 
wear shoes, has a ring, &c. It should be noted, however, that 
'clothes,' 'shoes/ &c, do not of themselves imply habit ; this 
is only predicable of them when possessed. 

Action includes all the varieties of causes, or all the ways 
in which objects may produce changes in others. 

Passion includes whatever implies the notion of suffering, 
and all the varieties of effects, or the ways in which objects 
may undergo changes. 

Various objections have from time to time been made to the 
Aristotelic enumeration of the categories, and probably upon 
satisfactory grounds ; it is questionable, however, whether a 
more satisfactory classification has yet appeared. The Aristo- 
telic categories are adopted here, as deduced and simplified by 
SirW. Hamilton : 'They' (the ten categories) 'are all divisions 
of being, — ens. Being is divided into ens per se, and ens per 
accidens. Ens per se corresponds to substance, the first of the 
Aristotelic categories. Ens per accidens comprises the other 
nine ; for it either denotes something absolute or something 
relative. If something absolute, it either originates in the matter 
of the substance, and is divisible — quantity, Aristotle's second 
category; or in the form, and is indivisible — quality, Aristotle's 
third category. If something relative, it constitutes relation, 
the fourth category ; and to relation the other six may easily 
be reduced. For the fifth, where, denotes the relation be- 
tween different objects in space, or the relation between place 
and the thing placed. The sixth, when, denotes the relation 
between objects in succession, or the relation between time 



68 MANUAL OF LOGIC. 

and a thing in time. The seventh, posture, is the relation of 
the parts of a body to each other. The eighth, having, is the 
relation of the thing having and the thing had, while the ninth 
and tenth, action and passion, are the reciprocal relations be- 
tween the agent and the patient. There are on this scheme one 
supreme category — being; two at the first descent, ens per se, 
ens per accidens, four at the first and second, substance, quantity, 
quality, relation, and to the dignity of category these four are, 
of Aristotle's ten, pre-eminently, if not exclusively, entitled.' 

Locke has reduced all things to three classes, viz., sub- 
stances, modes, and relations. 

Hume classifies all things under the two categories of ideas 
and impressions. 

Kant's list amounts to twelve, viz., unity, plurality, totality, 
affirmation, negation, limitation, independence, dependence, 
interdependence, actuality, possibility, and necessity. 

Mr Mill's categories are four in number, viz., 1. Feelings, 
or states of cousciousness ; 2. Minds which experience these 
feelings ; 3. Bodies or external objects which excite certain 
of these feelings, together with powers or properties whereby 
they excite them ; and, 4. The successions and co-existences, 
the likenesses and unlikenesses, between feelings and states 
of consciousness. 

The author of the ' Outline of the Laws of Thought ' pro- 
poses the following scheme : — ' Conceivable things,' he says, 
' are substance and attribute.' He subdivides attribute into 
quantity, quality, relation, and relation into that of time, of 
space, of causation, of composition, of agreement and repug- 
nance, of polar opposition, of finite to infinite. 

' Most of these names,' he remarks, l will be easily under- 
stood : the relation of polar opposition may not be so. We 
find that, in different parts of the field of knowledge, pairs of 
things unite and form a new whole different from either of 
them.' He gives, as examples, the doctrine of the Mean in 
morals ; in chemistry, the neutral salts, &c. 



MANUAL OF LOGIC. 69 

A facetious mathematician, of the last age, was of opinion 
that all the predicaments of the peripatetics might be substi- 
tuted by these two, viz., data and qucesita* 



SECTION V. 



Division literally signifies the separation of the component 
parts of some really existing whole, as when we divide a tree 
into its several parts ; as, root, trunk, branches, &c. 

In a division of this nature, each of the parts is strictly and 
properly a ' part,' and is really less than the whole ; for it 
cannot be affirmed of any part separately, that it is a 'tree.' A 
whole of this description is said to be a real or physical 
whole. It follows that physical division can only be applied 
to individuals. 

As recognised in logic, division is used in a figurative 
sense, and means the distinct, i. e., the separate enumeration 
of the several things signified by a common term, c It is 
therefore on common terms only, as denoting classes, that 
logical division can operate. A whole of this kind is said to 
be an ideal or metaphysical whole. 

If we consider the common term tree as a genus, and 
proceed to divide it, the word ' division ' will be used in its 

a It is still an open question whether the categories ought to be referred to 
metaphysics, logic, or grammar. The weight of opinion is, however, in favour 
of their being considered a metaphysical distribution. 

b Boethius is the chief authority on the doctrine of ' division.' His treatise 
de divisione is founded on a work on the same subject by Andronicus Ehodius, 
a peripatetic. 

c Distincta enumeratio plurium quae communi termino significantur. — 
Aldrich. 



70 MANUAL OF LOGIC. 

figurative sense ; for since there is nothing in nature corres- 
ponding to the common term 'tree,' it follows that it cannot be 
divided into really existing parts. The only division of which 
it is susceptible is the distinct enumeration of the several 
species contained under it — such as oak, elm, ash, birch, fir, 
&c. These are called parts, but they are so in a figura- 
tive, not in a real sense, since each of the parts, as regards 
comprehension, is greater than the whole divided, for in 
addition to the common nature (i. e., the genus) predicable of 
oak, elm, &c, each of them implies a differentia or distinguish- 
ing characteristic, which is not predicable of the genus ' tree.' 
This kind of division is distinctively named logical division. 

It follows, from the nature of logical division, that any 
term denoting some really existing individual thing cannot 
be logically divided ; and hence a term of this description is 
in logic termed indivisible (aro/jbov), but any term denoting a 
genus admits of logical division. To enumerate, therefore, 
the various co-ordinate species of which a genus is composed, 
is to divide such genus. a 

a Logicians enumerate wholes of various kinds. 1. A Logical or universal 
whole is a genus. The genus animal may be divided into men, beasts, birds, 
fishes, and insects. A whole of this description is termed universal, as the term 
denoting it must be a common or universal name. 2. An essential whole is one 
to which all its parts are essential ; the parts are said to be constitutive (partes 
constitutive), and if from an essential whole any of the parts be taken away, 
the whole is destroyed, as all the parts are essential to its existence. An essen- 
tial whole is either physical or metaphysical. A physical essential whole is made 
up of parts that have real existence, e. g., a body consists of matter and form ; 
a man consists of a human body and a rational soul. A metaphysical essential 
whole is one whose parts have no real existence. It is the same with the logi- 
cal whole explained in the text. 3. An integral whole is some actually existing 
thing, and consists of integrant parts (partes integrantes), and these, according 
to the nature of the wholes, may be members, parts, or particles, e. g., the 
human body is an integral whole, consisting of head, arms, legs, &c. ; a book is 
an integral whole, the parts of which are leaves, back, cover, &c. When an in- 
tegral whole is made up of particles of the same kind, as a slab of marble, it is 
called a homogeneous whole ; but when it consists of parts or members, it is 



MANUAL OP LOGIC. 71 



RULES OF LOGICAL DIVISION. 



1. The parts, i. e., the constituent species, must together 
be equal to the genus divided. 

The following are examples of logical wholes, where the 
constituent species taken together are equal to the whole 
divided : — The imponderable bodies are ' light,' ' caloric,' 
{ electricity.' Oratory is either ' deliberative/ ' forensic,' or 
' demonstrative.' Theology is either ' biblical,' ' systematical,' 
or ' historical.' 

2. The constituent species, i. e., the dividing members, 
must exclude one another. 

This rule is merely a caution against any contravention of 
the first, and it can be best illustrated by examples, in which 
the dividing members (membra dividentia) do not exclude 
one another, e. g., suppose we divide cause into efficient, 
material, formal, final, and instrumental, the members of the 
division would not exclude one another, for the * instrumen- 
tal ' is included in the ' efficient.' Or let the whole to be 
divided be imaginative writers. Now if we divide these into 
the species ' poets/ ' dramatists/ and * writers of fiction/ 
the parts do not exclude one another, i. e., they are not 
opposed, for some poets are dramatists, and some works 
of fiction are rythmical. Again, should we divide govern- 
ment into patriarchal, despotic, monarchial, democratic, and 
republican, the dividing members would not exclude or be op- 
posed to one another ; for a patriarchal government may be 
despotic, and vice versa, and a democracy and a republic can 
only differ in accidental circumstances. 

called a heterogeneous, whole. An integral whole may be deprived of a non-essen- 
tial part, without injuring its existence. — [This note is, in substance, taken 
from Wallis and Sanderson.'} Any species subalterna may be considered a 
logical whole, as classes are its contained parts. A species infima is not, 
however, a logical whole, as its subject parts are individuals, not classes, and 
individuals are distinguished by accidents, not by differentiae. 



72 MANUAL OF LOGIC. 

The Porphyria!! division of the predicables into genus, 
species, differentia, proprium, and accidens, is a correct and 
familiar exemplification of this rule. On the other hand, the 
operations of the mind, viz., simple apprehension, judgment, 
and reasoning, would be a cross division, inasmuch as judg- 
ment is presupposed in simple apprehension as well as reasoning. 

3. The division must proceed on one principle.* 

This rule has particular reference to the point of view in 
which we are to consider the whole to be divided, e. g., 
animals may be divided on one principle (fundamentum 
divisionis) into rational and irrational, on another principle 
into gressilia, volatilia, natatilia, reptilia, and zoophyta, or, 
again, into cold-bloodied and warm-blooded. If, however, we 
were to intermix the members of these several modes of divi- 
sion, we would be introducing a different principle from that 
which we set out with, and, consequently, the division would 
be incorrect. b 

But the above refers merely to wholes of extension. There 
are also wholes of comprehension. In the former we separate 
or enumerate the co-ordinate species ; in the latter we resolve 



a We must be careful to keep in mind the principle of division with which we 
set out, e. g., whether we begin dividing books according to their matter, 
their language, or their size, &c, all these being so many cross divisions. And 
when anything is capable of being divided in several different ways, we are not 
to reckon one of these as the true, or real, or right one, without specifying 
what the object is which we have in Miew ; for one mode of dividing may be the 
most suitable for one purpose, and another for another, as one of the above 
modes of dividing books would be the most suitable to a bookbinder ; another 
in a philosophical, and another in a philological view. — Wkateley, book II. 

b The principle of division mentioned is the point of view from which we are 
to regard the conception to be divided ; for we may divide one many times in 
various points of view. Thus man may be divided into European, Asiatic, 
African, American, and Australian, or, again, into Christian, Mahometan, and 
Pagan, or, again, into just and unjust ; and in the first division locality, in the 
second religion, and in the third behaviour, is the principle of division. — Outline 
of the Laws of Thought. 



MANUAL OF LOGIC. 73 

the more complex conception into the simple conceptions of 
which it is composed. The one analyses the extension or 
denotation, the other the connotation of a term. In a whole 
of comprehension* we divide, as it were, the ideas or concep- 
tions ; whereas in a whole of extension we separate the 
species. 

The following are examples of wholes of comprehension : — 
Goodness of memory may be resolved into the conceptions 
of ' susceptibility,' * retentiveness/ and ' readiness ;' Repen- 
tance into 'confession,' * contrition/ and 'amendment;' 
Gratitude into a ' consciousness of favour received,' ' a dispo- 
sition to acknowledge it on every proper occasion/ and ' a 
resolution to seize the first opportunity of returning a similar 
favour to the benefactor.' 

Boethius enumerates three kinds of division, — 1st, The divi- 
sion of a genus into its subject species, which is distinctively 
named logical division, as mentioned above. 2d, The division 
of a whole into its parts, corresponding to physical division, 
with this difference, that Boethius includes under this head 
the individuals contained under an infima species, which 
must be referred to logical division, if to any ; but the diffi- 
culty of enumerating the number of individuals contained 
under it, would render it in almost every case impracticable ; 
and, 3d, The division of an equivocal term into its various 
meanings. This species of division is sometimes termed dis- 
tinction, and is restricted to the division of equivocal terms 
or names; it amounts to nothing more than an explanation 
of the various senses in which an equivocal term may be un- 
derstood. b In many cases a perfect division may be obtained 

* The parts of a whole of extension are connected by a disjunctive conjunc- 
tion, and of a whole of comprehension by a copulative conjunction. — Wytteribach . 

b The test of this is, that the name is predicable of each member, but not the 
same definition. — Mansell, p. 30. 

It may be observed, that it is frequently necessary, in examining the argu- 
ments of another, to mark the different senses in which we may understand a 

D 



74 MANUAL OP LOGIC. 

by the use of the definite and indefinite nouns. As already 
stated, a noun is said to be indefinite to which the particle 
'noti' is prefixed, and definite when this particle is not pre- 
fixed. By this manner of division, a whole is divided into 
two parts, one of which must be immediately opposed to 
the other, e. g., men may be divided into those who 
are Europeans and those who are not Europeans ; ani- 
mals into bipeds, and not bipeds, or into rational, and 
not rational, or irrational. A logical division of this kind, 
according to the old logicians, has a Nomen Finitum, the name 
of an exhaustible kind, on one side, and a Nomen Infinitum, 
the name of an inexhaustible kind, on the other. This divi- 
sion into two members, usually termed dichotomy (6/^/oro/x/a), 
from its simplicity, shows more readily and plainly than any 
other, that the dividing members are distinct and opposed; for 
the union of the two members will be equivalent to the whole 
divided, and secures, therefore, the requisites of good division 
mentioned in the two first rules. a On the other hand, however, it 
is comparatively useless, because of one of the dividing mem- 



word or proposition that we employ, and to distinguish them carefully. For 
instance, a proposition may in one instance be true, and in another false or 
doubtful. And many writers take advantage of this ambiguity, confounding 
the two senses, displaying its truth and certainty, in the sense which is indu- 
bitable, but which perhaps makes nothing for their argument, and then apply- 
ing it to their argument in the other sense, in which it is by no means true or 
certain. — Walker's Commentary, cap. 10. 

a Cicero mentions only two kinds of division, viz., partition and division, and 
explains their respective significations thus: ' Sed quid inter se differant planius 
dicendum est. In partitione quasi membra sunt, ut corporis, caput, humeri, 
manus, latera, crura, pedes, et cetera ; in divisione, formae sunt, quas Graeci 
tdsocg vocant ; nostri, si qui haec forte tractant, species appellant. — Top., 
cap. 6, 7. 

A rule of division often laid down is, that it should be into its proximate 
parts, i. e., that the dividing parts should be of the same degree in the predica- 
mental line, no one of them of a higher species than the others; in other words, 
that they should be equidistant from some common antecedent genus. 



MANUAL OF LOGIC. 75 

bers, and that generally the larger, we know nothing, except 
that it wants the leading characteristic of the other ; in other 
words, a differentia is affirmed of one of the parts into which 
a whole is thus divided, but denied of the other ; so that we 
can only have a distinct conception of one of the parts, viz., 
that which has the differential attribute. All we can know 
of the other part is, that it is not contained in the class speci- 
fied by the differentia. Division by dichotomy, or bipartite 
division, is usually attributed to Peter Ramus. He and his 
followers were attached to it ; but it had been a favourite with 
Plato and others long before his time. Both Plato and 
Ramus used dichotomy by contradiction. Aristotle approved 
of that by contraries, but rejected that by privative and inde- 
finite terms. Boethius sanctions the use of contraries, contra- 
dictories, and also positive and privative terms, but discards 
relatives. 

Those who hold logic to be purely a formal science, must of 
necessity hold division by dichotomy to be the only logical 
mode, for any other description of division implies a know- 
ledge of the matter of the whole divided. It may be fairly 
questioned, however, whether division by dichotomy, as well 
as other modes, does not imply a knowledge of the matter, 
although possibly in a more restricted degree. 



SECTION VI. 

DEFINITION. 

Definition (ogi6(j.og) literally signifies the laying down the 
boundary of a thing ; but in logic it signifies an expression 
of thought in language which so explains a term as to sepa- 
rate it from any other, and thus to lay down, as it were, the 
limit of its signification ; like division, it is used in a figura- 
tive sense. 



76 MANUAL OF LOGIC. 

Correct definition subserves a two-fold object. It either 
conveys to the mind of a hearer the exact conception which 
the term defined represents, or it may correct any indistinct 
or inaccurate notion he may have previously entertained re- 
garding it. The first object presupposes that the hearer is 
altogether ignorant of the meaning of the word or thing 
defined ; the second implies that a conception is conveyed to 
his mind more correct than that previously entertained. 

Definitions are of two kinds, viz., nominal and real. 

In nominal definition we merely explain the meaning of a 
term, with the view of guarding against ambiguity in the use 
of it, or misconception of its exact import. In this case the 
meaning of the term to be defined must be explained by some 
equivalent expression, which must be more intelligible,* e. g., 

The Decalogue is the ten commandments. 

The Pentateuch is the five books of Moses. 

A telescope is an instrument for viewing distant objects. 

In many cases, the nominal and real essence of a thing 

a Nominal definition, as understood by Aldrich, ' Homo, qui ex liumo 
(an unfortunate example, by the way) should more properly be termed defini- 
tion by etymology, for it merely explains the original import of the word. It 
is questionable, however, whether a definition of this kind should be considered 
a definition at all, for in the modifications words undergo in meaning, as ap- 
plied in language, their etymological signification is often completely lost sight 
of. Definition, by a synonymous term, as ' honesty is probity,' is also com- 
paratively useless, for the synonym used to define may not convey a more dis- 
tinct conception than the definitum or thing defined. Neither of these methods 
is Aristotelic, although they can both be traced back to an early period. - 

In a rhetorical point of view, however, definition by etymology may be very 
effective. In Cicero's definition of fortitude, viz., ' virtus pugnans pro aequi- 
tate,' the remains of the original sense of virtus, manhood, give a beauty and 
force to the expression, which cannot be preserved when translated into another 
language. The Greek Apsryj, and the German Tugend, originally denoted 
strength, afterwards courage, and at last virtue. The happy derivation of vir- 
tus from vir, gives an energy to the phrase of Cicero, which illustrates the use 
of etymology in the hands of a skilful writer. 



MANUAL OF LOGIC. 77 

exactly coincide, i> e , the idea conveyed by the term is the 
same as the nature of the thing* Thus a triangle is 'that 
which has three sides,' which is both a nominal and real 
definition. 

In real definition we explain not only the meaning of the 
term, but also the nature of the thing signified by it. 

Real definition is of two kinds, accidental and essential, 
otherwise called imperfect and perfect. It is common to 
both that they are used in explaining things, not names. 

In accidental definition, we describe or enumerate some of 
the properties or accidents of what is implied by a term. 
This kind of definition is therefore usually termed descrip- 
tion. Any definition may be considered accidental, where 
only the genus and a property occur; for a property must in 
all cases be regarded as an accident, unless it is deduced from 
a known differentia. The following are examples of accidental 
definition.* 

A ball is a figure that has an aptitude to roll. 
Seat is the sensation produced by approaching fire. 
Wan is a risible animal. 

Animal is a body which can move itself from place to 
place. 

Ink is a liquid used for the purposes of writing and printing. 

Accidental definition is frequently the only method by 
which we are able to define a thing or term representing it, 
in consequence of our ignorance of the characteristic quality 
which constitutes the differentia. In such cases, we often find 
it necessary to enumerate a number of marks or attributes, 
the aggregate of which must be considered as the differentia, 
until we are able to single out some particular attribute suffi- 

a An accidental definition never includes a differentia. The conceptions 
embraced in it are tliose of a genus and one or more properties. Porphyry and 
Boethius reject it ; but it has been adopted by some more recent writers. A 
definition of this kind is properly description, and not definition. 



78 MANUAL OF LOGIC. 

cient of itself to distinguish its subject from all others. Cases 
of' this nature are constantly occurring in Botany, Natural 
History and Mineralogy. 

In essential definition we lay down the constituting parts 
of the essence. It is of two kinds, viz., logical, or metaphy- 
sical, and physical. In logical definition we lay down the 
ideal parts, i. e., the proximate genus and differentia. 

This is of all kinds of definition the most perfect. It fol- 
lows that any term that can be logically defined must be 
expressive of a species. The following may suffice as 
examples : — 

Man is a rational animal. 

Rhetoric is the art of speaking persuasively. 

Slavery is compulsory subjection to a master. 

A parallelogram is a four- sided figure, the opposite sides 
of which are parallel. 

Belief is assent produced by apparent credibility. 

A proposition is a declaratory sentence. 

In physical definition, we lay down the really existing and 
distinct parts of an essence, i. e., parts that admit of actual 
separation. In essential definition this is not the case, for 
genus and differentia are only distinguished by the under- 
standing. The following are examples of physical defini- 
tion : — 

An animal is a living body, consisting of head, body, legs, &c. 

A tree is that which consists of root, trunk, branches, 
leaves, sap, &c. 

A house is a structure composed of foundation, walls, roof, 
chimneys, &c. 

For the sake of clearness, the various kinds of definition 
already exp!ained may be illustrated by one example : — 

Nominal. — A proposition is that which is proposed to the 
mind for its assent or rejection. 

Accidental. — A proposition is the verbal expression of an 
act of judgment. 



MANUAL OF LOGIC. 79 

Logical. — A proposition is a declaratory sentence. 

Physical. — A proposition is that which consists of a sub- 
ject, predicate, and copula. 

The following scheme presents the different kinds of defini- 
tion, as laid down by Aldrich, ' definition ' being used as the 
summum genus: — 

'Nominal, 

Definition, -j /Accidental, 

,Real,-{ /physical, 

Essential, \ Logical, or 

VMetaphysical. a 
The rules of definition are three — 
1. The definition must be adequate to the term defined. 15 
The conception intended to be conveyed by the definition 
must be exactly equal to the definitum or term defined. 
Hence the definition must neither be too extensive nor too 
narrow. It will be too narrow if it omit any essential attri- 
bute, and too extensive if it include any as essential attribute 
which does not belong to it. As in adequate logical division, 
the whole and the dividing parts should reciprocate ; so in 

a Aldrich illustrates the various kinds of definition thus : ' Man, nominally, 
qui ex humo ; accidentally, an unfeathered two-legged animal ; logically, a 
rational animal; physically, a being consisting of an organised body and a 
rational soul.' 

b A definition may be inadequate in two ways — either if it be not appli- 
cable to the whole thing defined, or if it be applicable to anything else than the 
thing defined. 

c There are three cases in which logical definition is inapplicable : 1. Summa 
genera, which have no higher genus, and consequently, no constitutive differ- 
ence; 2. Individuals which have no essential difference, and can only be defined 
by description, i. e., by enumerating the accidents belonging to individuals, 
whereby the differences between them and any other may be shown ; and, 3 
The names of simple ideas, viz., intuitions, which, from their nature, can have 
no complexity. 



80 MANUAL OF LOGIC. 

adequate definition the definitum and its definition should 
also reciprocate* i. e., be simply convertible. 

The adequacy of any definition may be tested in this way. 
The following are examples of adequate definition : — 

Wine, a juice extracted from grapes. 
Conscience, the faculty by which we judge of right and 
wrong. 

Pension, an allowance for past services. 

The following examples err by excess : — 

An insect is an animal that flies. 
Man is an intelligent being. 

In the first example the definition is too extensive, being 
applicable to birds as well as insects; in the second, the 
definition applies to all intelligences as well as to man. The 
definitum and definition are not, therefore, simply convertible, 
or do not reciprocate. 

The following examples, on the other hand, err by defect : — 

Man is a civilised, rational animal. 

Here the definition is too narrow, for it excludes uncivi- 
lised man. 

A religious person is one who holds the peculiar doctrines 
of Calvin. 

This definition is also defective, for many persons who 
must be accounted religious reject some of Calvin's doctrines. 

2. The definition must in itself a be clearer than the thing 
defined. 

ft It has frequently been objected to metaphysical definition, that it is not 
clearer, in most cases, than the term defined ; and when the term which is to 
be defined is very familiar to the hearers, this certainly is the fact. Thus the 
word man is more familiar to the ear, and is accidentally better known than 
the term rational animal; but yet the words 'rational animal ' are in their 
nature more clear and better, known than the word ' man,' inasmuch as they 
convey less complicated ideas. — ffuyshe, p. 44. 



MANUAL OF LOGIC. 81 

It is necessary that the definition should convey a clearer 
idea than the definitura, otherwise it would not explain it ; 
and it is one of the objects of definition to explain a term im- 
plying a complex conception by other terms implying less 
complex conceptions, or, at all events, better known. 

The following examples offend against this rule : — 

Net-work, anything reticulated or decussated with inter- 
stices between the points of intersection.* 

Species is the identity of determinate form, cardinal pro- 
perties, and organific or constitutive law. b 

3. The definition must be included in a just number of 
proper words. 

By proper words (voces propria) Aldrich means words 
sanctioned by common usage, d in contradistinction to meta- 
phorical and obsolete phraseology. The terms which com- 
pose the following definitions are metaphorical : — 

Old age is the evening of life. 

A warrior is a thunderbolt of war. 

The following examples are characterised by undue 
brevity : — * 

A chariot is a vehicle. 

A cascade is a waterfall. 

Money is coin. e 

a Johnson. b Tappan. 

c Nam ex Metaphoris oritur ambiguitas, ex prolixitate, confusio — for from 
metaphorical terms there would rise indistinctness or ambiguity, from undue 
brevity obscurity, and from too great prolixity confusion. — Aldrich. <7rav yap 
aaatpig to kcltol psroxpogav Xsyopsvov, t&lv yag ctffcMpeg to [JjY\ eiwfog 
— for everything is deficient in precision and clearness which is spoken meta- 
phorically, or in language not sanctioned by common usage. — Artistotle. 

d %'jpia ovo/xetra, otherwise called established names (xsz/xgya ovo/tara). 
— Aristotle. 

e These instances exemplify what is called by some, definition from change 
of symbol, where both subject and predicate are symbolical conceptions — the 
latter being given as a substitute for the former on a principle of expedience 
only. — See Outline of the Laws of Thought, p. 160. 

D 2 



82 MANUAL OF LOGIC. 

The subjoined examples, on the other hand, are vitiated by- 
unnecessary prolixity : — 

Astrology is that curious science, so much in vogue during 
the middle ages, which instructs mankind in the supposed in- 
fluences which the stars possess over human circumstances 
and actions, and by which they rule and direct the world. 

Money is that useful species of property which, by serving 
as a common measure, by which all the necessaries, all the 
conveniences, and all the luxuries of life may be estimated 
and procured, becomes itself the great essential, and com- 
prises within itself all that can be thought needful to render 
life desirable. a 

Aristotle's view of definition is threefold. 1. The defini- 
tion of a thing as it is in itself (Xoyog rov n stfri), correspond- 
ing to the Real Definition of more recent logicians. This kind 
of definition is first applied to substances which exist per se; and 
as their existence is assumed, not demonstrated, their defini- 
tion is said to be unsusceptible of demonstration (avaKodsrtrog), 
2. The definition of an attribute. This is also a definition 
(tov ri sari), with this difference, that the existence of an 
attribute is not assumed, but demonstrated to exist in the 
substance, or subject of inhesion, and the demonstration con- 
sequently proceeds on the assumption of the existence of the 
subject : in other words, the cause of the attribute is sought 
in the subject. This is illustrated by defining an eclipse. — 
Why is the moon eclipsed ? Because the sun's light is inter- 
cepted by the earth. Consequently, to the question, What is an 
eclipse of the moon? the answer (i. e., the definition) will be, 

a If a definition be chargeable with tautology, it is incorrect, though without 
offending against the two rules. Tautology consists in inserting too much, not 
in mere words, but in sense. Thus to define a parallelogram, a ' four-sided 
figure, whose opposite sides are parallel and equal,' would be tautological, 
because though it is true that such a figure, and such alone, is a parallelogram, 
the equality of the sides is implied in their being parallel, and may be proved 
from it. — Whateky, book II., cap. 5. 



MANUAL OF LOGIC. 83 

The interception of the sun's light from the moon by the earth. 
This demonstration is capable of being reduced to syllogistic 1 " 
form ; but as it stands, it differs from demonstration, as stated 
by Aristotle himself, in the arrangement or position of the 
terms (dsatg), or grammatical variety of form (truing), 3. 
Nominal definition, or, according to others, imperfect Eeal 
Definition. Aristotle's explanation of it is, rrjg rov n e&nv 
avobufyug (fv/jwsgatifAa — the conclusion of the demonstration 
of what a thing is. As Aristotle objects to nominal defini- 
tion, on the ground that it furnishes no proof of the actual 
existence of the things to which it applies, and as in many 
cases the nominal and real definition of a thing may nearly 
or altogether coincide, the latter opinion, viz., that of imperfect 
real definition is here considered to be meant by him. His 
views on the whole doctrine of definition are, however, ob- 
scure. 



SECTION VII. 

OF THE DISTRIBUTION OF TERMS. 

The subject (pKOTteifisvov) is distributed in all universal pro- 
positions, and the predicate in all negative propositions, since 
in the former the entire conception is included, while in the 
latter the entire conception is excluded. In considering 
terms with reference to their distribution, there are two rules 
which it will be necessary to remember : — 

1. All universal propositions (and no particular) distribute 
the subject. 

2. All negative propositions (and no affirmative) distribute 
the predicate. 

When we say that a term is distributed, we mean that it is 

a Omne corpus naturale illuminatum a sole, privatum luce a terrae object u 
deficit; luna est hujusmodi, ergo luna deficit. — Aquinas. 



84 MANUAL OF LOGIC. 

used in its fullest extent ; that it stands for all its significates, 
viz., the several things which it signifies or to which it is 
applicable. 

1. Of the Subject. 

In all universal propositions, whether affirmative or nega- 
tive, the subject must be distributed; for this is the differentia 
of a universal proposition viewed as to its quantity. In the 
^proposition, 

All tyrants are miserable, 
the common term ' tyrants ' includes Dionysius, Phraates, 
Nero, and every other individual answering to the descrip- 
tion ; in other words^ it stands for the whole of its signifi- 
cates. When, again, we say, 

No islands are surrounded by water, 
everything of which the common term * island ' can be 
affirmed is excluded from the application of the predicate 
1 surrounded by water ;' in other words, none of the signifi- 
cates of the term < island ' agrees with the predicate. 

Since the distribution of the terms of propositions is indi- 
cated by the universality of the subject or the negative cha- 
racter of the proposition, it is manifest that in all particular 
propositions the subject is undistributed* as it stands only for 
a part of its significates, being restricted to this either by its 
indefinite character or some qualifying term. In the example, 

Some islands are fertile, 
the term ' island/ though applicable in its unrestricted sense 
to Iceland, and all barren islands, yet, as used in this propo- 
sition, it does not embrace these among its significates, as it 
only contains in its extension such islands as may be affirmed 
to be fertile; and hence it is not distributed. In the ex- 
ample, 

a Where we represent, judge of, or reason from a whole conception, it is said 
in technical language to be distributed; where a part only is treated, we call it 
undistributed. — Outline of the Laws of Thought, p. 138. 



MANUAL OF LOGIC. 85 

Some critics are not candid judges, 
the subject * critics ' is also used in a restricted sense, for it ex- 
cludes from its extension all such critics as are candid judges. 

It is evident, therefore, that the distribution or non-distribu- 
tion of a term depends on its quantity, and not on its quality. 

It follows from the foregoing, that the subject of an inde- 
finite proposition, in necessary matter, is distributed. In the 
example, 

Angels are incorporeal, 
although there is no sign of universality prefixed to the sub- 
ject, yet, as it is in necessary matter, we are warranted to 
affirm the predicate of all angels. 

The subject of an indefinite proposition, in contingent mat- 
ter, on the other hand, is undistributed. In the example, 

Misfortunes are unavoidable, 
we know from the matter that the subject must be taken in a 
restricted sense, and that all we can affirm is some misfor- 
tunes, &c. 

2. Of the Predicate. 

The predicate (xarriyogovpsvov) of an affirmative proposition, 
with few exceptions, is never distributed. In the following 
example of a universal affirmative, viz., 

All metals are fusible, 
the predicate ' fusible ' is not distributed ; for although it is 
affirmed of all metals, this does not exhaust its application, 
inasmuch as it is predicable of many other substances be- 
sides metals, and, consequently, it cannot be said to be wholly 
distributed, since the subject of the proposition does not ex- 
press all the substances capable of being fused. 

This is still more obvious in the case of a particular 
affirmative, e. g., 

Some vapours are luminous. 
Here the predicate 'luminous' is predicable not only of some 
vapours, but of an indefinite variety of bodies. 



86 MANUAL OF LOGIC. 

It happens occasionally that the perdicate is of equal extent 
with the subject, i. e., that the predicate fully distributed may 
be affirmed of the subject also fully distributed. The judg- 
ments expressed in propositions of this nature are said to be 
substitutive ; for since in them the predicate is used to define 
the subject, the whole of it must be given, otherwise it would 
be useless for definition. The subject and predicate are 
therefore exactly co-extensive, for they may change places in 
the judgment, so that the definitum may in its turn become 
a definition, e. g., in the example, ' Man is a rational animal,' 
no individual comes into the class of rational animals which 
is not also in man; and, conversely, no individual comes 
under man which is not also under rational animal ; for 
here both the subject and predicate are generalisations from 
the very same class of beings — the only difference being 
that the subject is symbolical, or the sign of a class, while 
the predicate is notative, that is, noting essential attributes. 

It is only in definitions that the subject and predicate are 
co-extensive, and this coincidence occurs wherever the predi- 
cate is a definition of the subject ; as, 

Rhetoric is the art of speaking persuasively. 
Or its logical difference ; as, 

All men are rational. 

A proposition is a declaratory sentence. 
Or a specific property ; as, 

A triangle is a figure having three angles. 

A proposition is a sentence signifying something true or false. 

Or in any case, in short, where the subject and predicate are 
simply convertible. 

In these examples the predicate may, in its distributed 
sense, be affirmed of the subject ; but it is to be observed 
that this circumstance cannot be inferred from the mere form 
of the proposition. It follows from the matter, not from the 
terms of the expression. 



MANUAL OF LOGIC. 87 

The judgment expressed by any proposition in which the 
subject and predicate are not co-extensive, is said to be attri- 
butive, as the predicate merely expresses an attribute not 
simply convertible with the subject, and cannot therefore be 
used to define the subject, e. g., 

Metals are fusible, 

Gold is heavy, 
are judgments in which this kind of predicate occurs. 

In negative propositions, whether universal or particular, 
the predicate must be distributed, otherwise the proposition 
could not be true, e. g., the proposition, 

Irrational animals are not morally responsible, 
would be false if any part of the predicate, ' morally respon- 
sible,' agreed with the subject, ' irrational animals.' 

In particular negatives, however, the distribution of the 
predicate is not so evident, e. g., the proposition, 

Some critics are not candid, 
asserts that there is a certain class of critics comprised in the 
subject, from which every individual of which the predicate 
can be affirmed is wholly excluded ; in other words, the pre- 
dicate ' candid,' in its most extensive signification, cannot be 
affirmed of any individual comprised under the particular 
class of critics denoted by the subject. Consequently, the pre- 
dicate is used here in its universal, i. e., its distributed sense, 
and unless it were so, the proposition would not be true. 

No signs of universality or particularity are prefixed to the 
predicate, because in affirmative propositions its non-distribu- 
tion is indicated by the affirmation, and in negative proposi- 
tions its distribution is indicated by the negation. 
~_ It has been shown above that a term may consist of one 
word, or several ; but the only terms consisting of one word, 
which can be used as the subjects or predicates of proposi- 
tions, are nouns substantive in the nominative case. We may 
add here that the infinitive of a verb, a certain form of which 
is only one word, may also be used as a term in a proposition, 



88 MANUAL OF LOGIC, 

being equivalent to a noun -substantive. In English, in ad- 
dition to the usual form of the infinitive, which may be 
used as a term in a proposition, there is another, ending in 
' ingf synonymous with the ordinary form, e. g., ■ Instructing 
the ignorant is praiseworthy/ and 'It is praiseworthy to 
instruct the ignorant,' are equivalent propositions. 

This kind of infinitive is of the same form and sound as 
the participle present, but it can always be distinguished from 
it in this way, viz., when the usual form of the infinitive can 
be substituted for it without injuring the sense, it is the infi- 
nitive in l ing;' but when this substitution cannot take place 
without injuring the sensej then it is the participle present. 

The infinitive in ' ing ' may be used as a categorem, i. e., 
as a word having enough of independent meaning in itself to 
constitute a term, as. 

Seeing is believing; 
or it may be used as a syncategorem, i. e., as constituting a 
term in connection with other words, e. g., 

Accuracy in observing individual facts is necessary to cor- 
rect induction. 

It may be remarked, that the infinitive is often the predi- 
cate of a proposition ; but this never happens except when 
another infinitive is the subject, e. g., 

To imitate, is to admire. 

To bear, is to conquer our fate. 

To be loved, is to be happy. 

Laborare est orare. 

It may be remarked, that neither the infinitive, which is 
properly a noun-substantive, nor the participle, which is a 
noun-adjective, is included under the word ' verb,' for strictly 
speaking they are verbals, i. e., they have a relation to their 
verbs in signification, but they differ from them in the mode 
of signification. This arises from the circumstance that 
affirmation, which is essential to a verb, is not an attribute 
either of an infinitive or a participle. 



MANUAL OF LOGIC. 89 



CHAPTER III. 



SECTION I. 



JUDGMENT. 



Having already considered the first head of the logical dis- 
tribution of the cognitive faculties, viz., Simple Apprehension, 
and having treated of notions as simple or complex, of terms 
as singular or common, together with their names and classi- 
fications, as well as the logical instruments whereby we ac- 
quire distinctness in the apprehension of the meaning and use 
of terms, we now proceed to the second head, viz., Judgment. 
Under this head, we consider the mind not only as possess- 
ing notions distinctly, but as capable of comparing them to- 
gether, and of asserting some relation between them, whether 
of agreement or disagreement. While such assertion remains 
purely a mental act, it is called a judgment; but when it is 
expressed in words, it is termed a proposition. 

OF SIMPLE PROPOSITIONS. 

A proposition is defined by Aldrich to be ' Gratio indica- 
tive congrua et perfecta verum vel falsum significans sine 
ambiguitate,' — an asserting sentence grammatical and perfect, 
signifying something true or false, and free from ambiguity. 
This definition is of a mixed nature. It is partly metaphy- 
sical, and partly accidental. It is metaphysical, in so far as 

a Xoyog ot,iro<pavri'KOi. — Aristotle. Oratio enunciativa. — Boethius. 



90 MANUAL OF LOGIC. 

it defines a proposition to be an asserting sentence (oratio 
indicativa) ; but it is accidental, in so far as it states it to be 
true or false — and accidents should be excluded from the 
definition of what is implied by a common term. 

This objection to the definition of Aldrich may be removed 
by restricting the definition to the two first words, * oratio 
indicativa,' an asserting sentence ; for a proposition, logically 
defined, is a sentence which asserts, i. e., affirms or denies. 
This latter definition will consequently comprehend the whole 
essence of a proposition ; for a sentence is its genus, and 
asserting, i. e., affirming or denying, its difference. 

Since, therefore, a proposition must assert, i. e., affirm or 
deny some thing, all exclamations, interrogations, requests, 
and commands, &c, as no assertion is made in them, must be 
excluded ; as, for example, 

Oh ! how amiable are thy dwellings ! 

Do ye now believe °i 

Give me thy heart. 

Love thy neighbour as thyself. 

In a legitimate proposition, the four following conditions 
are requisite: — 

1. With regard to the words, it must be a sentence which 
affirms or denies ; as, 

All beasts of prey are carnivorous. 
The earth is not a plane. 

2. In respect of signification, it must signify something 
true; as, 

The air is elastic ; 
or false ; as, 

Moonlight is cold. 

3. A proposition must not be ambiguous ; in other words, 
it must not admit of dubious construction ; for if it did, it 
would be more than one sentence, and instead of being ' oratio 
indicativa,' an 'asserting sentence,' it would be 'orationes in- 
dicative,' ' asserting sentences.' 



MANUAL OF LOGIC. 91 

Any proposition of an ambiguous nature, i. e,, capable of 
being construed in more ways than one, must be a double 
sentence ; and this ambiguity is usually produced by equi- 
vocal words ; as, 

That is a bull. 

That is a bar. 
For the predicate in each of these propositions may be used 
equivocally. 

4. A proposition must not be ungrammatical ; for in this 
case it might be unintelligible. In proverbs, and elliptical 
sentences, the meaning may be intelligible, while the proposi- 
tion itself cannot be strictly termed complete, e. g., 

A word to the wise, 
as a proposition, is incomplete in form, but not in sense. The 
same ellipsis is adopted in the Latin — 

Verbum sat sapienti. 
The corresponding French proverb — 

Le sage entend a demi-mot, 
is complete in form as well as in sense. 

Division of Propositions. 

Propositions are divided according to their substance,* 
their quality, and their quantity. 

1 . Of the substance of Propositions. 

With regard to their substance, • propositions are of two 
kinds, viz., categorical b and hypothetical. 

a Relation, quality, quantity. — Kant. 
b The division of propositions into categorical and hypothetical, is not Aris- 
totelian. In every instance in which xaryjyogr/tog occurs in the organon of 
Aristotle, it signifies affirmative, and is used by him not as opposed to hypothe- 
tical (g£ v<7rok<KCiog), but to the words aftotparixog and grs^nxog, which 
signify negation ox privation. The meaning usually attached to ' categorical,' 
viz., an unconditional assertion, whether affirmative or negative, is supposed to 
have originated with Theophrastus, and is therefore not of Aristotelian origin. — 



92 MANUAL OF LOGIC. 

1. Categorical Propositions. —A categorical proposition 
asserts absolutely, i. e., unconditionally ; as, 

Music is the elocution of poetry. 
Honesty is the best policy. 
Man is not omniscient. 

Categorical propositions are of two kinds, viz., pure and modal. 
A pure categorical proposition simply asserts whether the 
subject does or does not agree with the predicate ; as, 

Virtue is its own reward. 
Benevolence is not the whole of virtue. 
Man is not infallible. 

A pure categorical proposition is sometimes called propo- 
sitio de inesse, because it simply states whether the predicate 
is or is not (metaphysically) in the subject. A modal cate- 
gorical proposition expresses in what mode or manner the 
subject does or does not agree with the predicate ; as, 

This man may perhaps be religious. 

No man can be altogether disinterested. 

A prejudiced historian will probably misrepresent the truth. 

The modality of a proposition affects the copula. 

Modal propositions may be reduced to pure categoricals by 
either considering the word which expresses the mode as 
united to the predicate, and thus forming a part of it ; as, 

Man is necessarily an animal ; 
or sometimes by attaching the word denoting the mode to the 
subject, which may be done when the mode only expresses 
whether the matter of the extremes be necessary, impossible, 
or contingent ; as, 

A fish lives necessarily in the water ; 
which means, 

[See Ed. Rev., vol. 57.] The division of propositions, however, into categorical 
and hypothetical, can scarcely be considered a cross one ; for all assertions must 
be made either with or without a condition. 



MANUAL OF LOGIC. 93 

All fish live in the water. 

A profligate man may possibly repent, and be saved ; 
which may be thus stated — 

The repentance and salvation of a profligate man is a thing 
that is possible.* 

Modal propositions will be more fully treated of hereafter, 
and in a different point of view. 

2. Of the Quality of Propositions. 

The quality of a proposition is of two kinds, essential and 
accidental. 

The quality of the expression of a proposition constitutes 
its essential quality; because affirmation or negation forms 
the logical difference or formal part of the essence, and is the 
only differentia from which all the propria may be deduced. 

The quality of the sense is the accidental quality ; because 
the expression of truth and of falsehood is the property, and, 
consequently, only an adjunct to the essence. 

When the term quality is used concerning propositions, with- 
out any distinguishing epithet, the essential quality is signified. 

The essential quality of a proposition is determined by the 
copula ; and hence it must be carefully observed, when a sign 
of negation occurs in a proposition, whether it really affects 
the copula. This may be done in any case, by analysing the 
proposition, and making allowance for the idiom of the language 
in which it is expressed. In a strictly logical point of view, 
the negative particle is always considered to affect the copula 
in whatever part of a proposition the idiom of any particu- 
lar language may place it ; and for this reason, propositions 

a Between the modality and matter of a proposition, logicians have made this 
distinction : Modality is an affection of the copula, and depends on the asser- 
tion; Matter is an affection of the terms, and depends not on the assertion, but 
on the actual relation of the things spoken of. In Aristotle's view, however, 
the modality of a proposition is to be looked for rather in the matter than in the 
enunciation. 



94 MANUAL OF LOGIC. 

virtually negative, although not so apparently, may, by logi- 
cal resolution, be reduced to a proper negative form, e. g., 

No brutes are morally responsible, 
may be resolved into 

Brutes are not morally responsible. 

On a similar principle, negative propositions may be re- 
duced to an affirmative form, by changing the place of the 
negative sign, and uniting it either with the subject or predi- 
cate, e. g., 

Minds are not material, 
may become affirmative by uniting the negative particle with 
the predicate, thus — 

Minds are, not-material ; 
and by another change of phrase, the same conception may be 
thus expressed — 

Minds are immaterial. 

Propositions which thus vary both in form and phraseo- 
logy, but in which the same conceptions are virtually ex- 
pressed, are designated equipollent propositions. 

According to their essential quality, propositions are divided 
into affirmative and negative. 

1. An affirmative* proposition is one which asserts that 
its extremes, viz., its subject and predicate, agree with each 
other ; in other words, that the predicate may be affirmed of 
the subject ; as, 

All true Christians are lovers of God. 

The English are the sovereigns of the ocean. 

Errors are marks of human infirmity. 

All philosophers profess to aim at the discovery of truth. 

2. A negative* proposition is that which asserts that its 
extremes disagree ; in other words, that the predicate cannot 
be affirmed of the subject ; as, 

a xaratpaGig stfrtv atfopavtiig rivog Kara, rivog. — Aristotle. 
b A<7ro(pa6ig sffriv atfotpavdig rivog wro r/vog. — Idem. 



MANUAL OF LOGIC. 95 

No miser is happy. 

All the troops united, were not able to defend the for- 
tress. 

A modest man cannot allege his own merits. 

A proposition is not negative, unless the particle of nega- 
tion immediately affects the copula. The following proposi- 
tions are therefore affirmative : — 

He who is not dishonest deserves our esteem. 

The man who sinneth not, is blessed indeed. 

Non injussa cano — I sing things not uncommanded. 

In English two negatives, connected in one sentence, make 
an affirmative ; as, 

No man is not mortal ; 
which is the same in meaning with man is mortal. But in 
Greek, and often in French, two negatives render the nega- 
tion intensive. 

According to their accidental quality, propositions are 
divided into true and false. This is said to be the proprium, 
inasmuch as it results from the essence of the proposition, 
i. e., from the difference or assertion. 

A true proposition is that which asserts what is the fact; as, 

Every good man is virtuous. 
All islands are surrounded by water. 

A false proposition is that which asserts what is not the 
fact ; as, 

A thief is trustworthy. 

All the planets are stationary. 

Truth is either logical or ethical. 

A proposition is logically true, when the relation predicated 
between a subject and a predicate actually exists. 

A proposition is ethically true, when its enunciation 
agrees with the judgment of the mind. If I say, 

This chiffonier is made of mahogany, 
and believe it to be so, the proposition is ethically true ; but 



96 MANUAL OF LOGIC. 

if it be merely veneered, the proposition is logically false. If 
the mind judge aright concerning things, the same proposi- 
tions will be both logically and ethically true. If the mind 
judge not aright, the proposition that is ethically true will be 
logically false, and the proposition that is logically true will be 
ethically false. 

3. Of the Quantity of Propositions. 

The quantity of a proposition means the extent to which 
the predicate is asserted of the subject. 

According to their quantity, propositions may be divided 
into universal, particular, singular, and indefinite* 

1. A universal affirmative proposition is that in which 
the predicate is affirmed of the whole of the subject ; and in 
this case the subject is taken in its whole sense, i. e., for 
everything signified by it, and is therefore said to be distri- 
buted. 

A term, whether used as a subject or predicate, is distri- 
buted or universal, when used in its widest signification, as 
being applied without limitation to every individual signified 
by it. 

Such distribution is indicated by some sign of universality, 
as all, every, whatever, &c, e. g., — 

All the metals are fusible by heat. 

All animals have the power of motion. 

Every intelligent being is responsible for his conduct. 

Whatever is produced by regular laws, is a proof of an in- 
telligent agent. 

2. An universal negative is a proposition whose subject is 
an universal term of the whole of which the predicate is 
denied. Its usual signs are no, none, neither, &c, e. g., — 

No conscientious person is deserving of ridicule. 
No human foresight can check the advance of old age, in- 
firmities, and death. 

a Instead of indefinite, Sir W. Hamilton recommends indesignate. 



MANUAL OF LOGIC. 97 

None of the ancient philosophers understood fluxions. 
Neither of the Bernoullis proved the case against Newton. 

The universality of a proposition is of two kinds, meta- 
physical and moral. 

A proposition metaphysically universal is that in which the 
predicate agrees with all the individuals contained in the 
subject, without exception ; as, 

Every man is an animal. 

All circles have a centre and circumference. 

All spirits are in their nature immortal. 

In each of these examples the predicate agrees with all the 
individuals of the subject, and we may therefore legitimately 
deduce from any of them either a particular proposition ; as, 
for example, 

Some men are animals ; 

or a singular proposition ; as, 

John is an animal. 

A proposition morally universal is that in which the pre- 
dicate agrees with most of the individuals of the subject, but 
not with all ; e. g. — 

All men prefer their own interest to the public. 

In this example the predicate, in its agreement with the 
individuals of the subject, admits of some exceptions. From 
this proposition, therefore, we may deduce a particular pro- 
position; as, 

Some men prefer their own interests to the public : 

but not a singular ; as, 

Aristides prefers his own interest to the public ; 

E 



98 MANUAL OF LOGIC. 

for the singular subject 'Aristides' may be among the indi- 
viduals with which the predicate does not agree (vide Subal- 
ternation of propositions). 

3. A particular affirmative proposition is that whose sub- 
ject is a universal term, with a particular sign prefixed, and 
of a part of which only the predicate is affirmed. The usual 
signs are some, many, most, few, several, there are, &c, e. g. — 

Some men of deep erudition confine their knowledge to 
their own breasts. 

Many men have raised fortunes, at the hazard of their lives. 

Most arbitrary monarchs are revengeful. 

Few men are truly wise. 

Several animals are amphibious. 

There are metals which are lighter than water. 

A particular negative proposition is that whose subject is 
a universal term, with a particular sign prefixed, and of a 
part of which only the predicate is denied. The usual signs 
are those of a particular affirmative with the particle not an- 
nexed to the copula, e. g. — 

Some offenders are not duly punished. 
Many authors are not men of original genius. 
Several troops were not armed. 
There are creatures which are not responsible. 

The subject of a negative proposition may have a universal 
sign, and yet the proposition may be equivalent only to a 
particular negative. In the following propositions, for ex- 
ample, — 

All men have not faith, 
All is not gold that glitters, 

the logical order should be, 

Not all men have faith. 

Not everything which glitters is gold. 



MANUAL OF LOGIC. 99 

Hence they are equivalent only to — 

Some men have not faith. 

Some things which glitter are not gold. 

There are some particular signs which make a near approach 
to a universal affirmative ; as, almost all, by far the greater 
part, &c, e. g. — 

Almost all the poets have been unfortunate. 
By far the greater part of men prefer private interest to 
that of the public. 

Some particular signs, on the other hand, render a proposi- 
tion almost equivalent to a universal negative; as, few, &c, 
e.g.— 

Few men, in this period of universal knowledge, attain to 
literary eminence. 

There are scarcely any who are free from the influence of 
some prejudices. 

4. A singular proposition is one whose subject is (1) 
either a singular term — as, 

Napoleon was a brave man ; 

Des Cartes was an ingenious philosopher ; 

Sir Isaac Newton was the author of the Principia ; 

Noah's ark contained animals of every species ; 

or (2) a singular pronoun ; as, 

Thou art the man ; 

Non omnis moriar, — I shall not altogether die ; 

or (3) a common term, with a singular sign, i. e., a univer- 
sal in the form of an individual — 

This fable is instructive ; 



100 MANUAL OF LOGIC. 

That general was defeated ; 

This man is occasionally intemperate ; 

or (4) when the subject consists of a number of nouns collec- 
tively understood ; so that they may be viewed as one single 
thing or body ; as, 

Caesar, Pompey, and Crassus constituted the first trium- 
virate. 

All the books in Ptolemy's library consisted of 200,000 
volumes, i. e., all together. 

The king, lords, and commons form a British parliament. 

The syncategorem all, when used distributively, is a sign 
of a universal proposition ; when it is applied in a collective 
sense, the proposition is singular; when it is distributive, its 
place may be correctly supplied by every or each ; as, 

All the colleges are governed by their respective statutes, 
i, e., each of the colleges. 

All the primary planets revolve in elliptic orbits about our 
sun as their centre. 

When it is collective, it admits of the introduction of the word 
together; as, 

All the colleges constitute an university, i. e., collectively 
taken. 

All the primary planets are eleven. 

In all singular propositions the predicate is asserted of the 
whole of the subject. Hence the subject is distributed, and 
singular propositions are considered as universals. 

5. An indefinite proposition has a common term for its 
subject ; but it has no sign expressed to indicate whether its 
subject is to be taken in a universal or particular sense ; as, 

Beasts have four feet, i. e., all beasts. 

A planet is ever changing its place, i. e., all planets. 



MANUAL OF LOGIC. 101 

The stars appear to us when the twilight is gone, i. e., 
those stars only which are above the horizon. 

Every indefinite proposition will admit either of an uni- 
versal or a particular sign, for the predicate must be asserted 
either universally or partially of the subject. But to deter- 
mine this, we must look to the matter of the proposition, 
as it is in this way alone we can ascertain the natural con- 
nection between the subject and the predicate. The matter a 
of a proposition is the extent of connection which naturally 
exists between the extremes, and it is of three kinds — neces- 
sary, impossible, and contingent. 

When the terms of a proposition agree essentially and in- 
variably with each other, it is said to be in necessary* matter, 
e.g.— 

All moral agents are responsible. 

& Those who hold logic to be a formal science must of course discard from its 
domain all consideration of real existence, and of the relations of real existence. 
Of the truth or falsehood of propositions in themselves, it is supposed to know- 
nothing, and can take no account of it. If this view of logic be correct, the 
matter and modality of propositions must be excluded from its province as extra- 
logical. ' If truth or falsehood,' remarks Sir W. Hamilton, ' as a material 
quality of propositions and syllogisms is extralogical, so also is their modality. 
Necessity, possibility, &c, are circumstances which do not affect the logical 
copula or the logical inference. They do not relate to the connection of the 
subject and the predicate, of the antecedent and consequent, as terms in thought, 
but as realities in existence ; they are metaphysical, not logical conditions. The 
syllogistic inference is always necessary ; it is modified by no extraformal con- 
dition ; is equally apodictic in contingent as in necessary matter.' — Ed. Rev., 
Vol. LVII. 

Kant sanctions the modality of propositions and syllogisms as necessary to be 
taken into account by the logician. Whateley's views of the province of logic 
are so contradictory that his authority on either side of the question goes for 
nothing. 

b There are three ways in which a predicate may be conceived of as neces- 
sary to its subject : — First, if it is an essential or formal quality — this is formal 
necessity ; — secondly, as being an inseparable deduction from some essential or 



1 02 MANUAL OP LOGIC. 

When the terms of a proposition differ from each other 
essentially and invariably, it is said to be in impossible 
matter, e. g. — 

No triangles are squares. 

When the terms of a proposition partly agree with each 
other, and partly differ, it is said to be in contingent mat- 
ter, e. g. — 

Legal enactments are beneficial to society. 

Of propositions implying necessary matter, affirmatives are 
true, and negatives false ; of those expressing impossible 
matter, negatives are true, and affirmatives false ; of those 
expressing contingent matter, universals are false and parti- 
culars true. 

In necessary and impossible matter indefinite propositions 
are reduced to the class of universals, and in contingent 
matter to the class of particulars. In the following example, 

Angels are incorporeal, 

the subject angels is not accompanied by any sign of univer- 
sality or particularity ; but as we cannot conceive of 'angels' 
as not being incorporeal, we affirm this predicate of all 
angels ; and hence the proposition is universal, the predicate 
being asserted of the whole subject. In the following proposi- 
tion, 

Human inventions are beneficial to society, 

there is no sign indicative either of universal or particular 
quantity prefixed to the subject ; but on examining the mat- 
formal quality — this is natural necessity ; — thirdly, as being incapable of being 
denied to it henceforward — this is necessity of fact. The first necessity is 
expressed, when we say that a quality is generic or specific— the second, when 
we call it a proprium — the third, when we say that a fact has become an inse- 
parable accident. — Moberly, p. 30. 



MANUAL OF LOGIC. 103 

ter of the proposition, we ascertain that the predicate cannot 
be affirmed of the whole subject, because the matter of the 
proposition is contingent ; and hence we can only assert, 

Some human inventions are beneficial to society. 

Since singular propositions may be considered as univer- 
sal, and since indefinite propositions can be reduced to uni- 
versal, if their matter is necessary or impossible, and to particu- 
lars, if their matter is contingent, it is unnecessary to consider 
either as a separate class of propositions ; for, strictly speaking, 
propositions, when viewed according to their quantity, may 
be divided into two kinds, viz., universal and particular. 

All pure categorical propositions, therefore, considered ac- 
cording to their quality and quantity, may be regarded as of 
four kinds, viz., universal affirmative, universal negative, par- 
ticular affirmative, and particular negative. These four 
classes of propositions are marked by the first four vowels, 
called symbols. Thus — 

A. Universal affirmative. 
E. Universal negative. 
I. Particular affirmative. 
O. Particular negative. 

The following scheme exhibits the relations of quantity 
and quality : — 

PROPOSITIONS. SUBJECTS. PREDICATES. 

Universal affirmatives, Universal, Particular. 

Universal negatives, Universal, Universal. 

Particular affirmatives, Particular, Particular. 

Particular negatives, Particular, Universal. 

In reference to the universality and particularity of the pre- 
dicates of propositions, the following maxims will be found 
in all cases to apply: — In negative propositions the predicate 
is universal by necessity. In affirmative propositions the pre- 



104 



MANUAL OF LOGIC. 



dicate is particular when it is only an attribute of the subject ; 
but it is universal when it can be substituted for, or reciprocate 
with the subject. 

The following scheme presents the division of propositions, 
with their sub-divisions : — 



f 



Substance 
into 



' Categorical,. 



Quality, 
namely, 



Quantity 
into 



Hypothetical,., 



( Essential, into... 



^ Accidental, into.. 



' Universal,. 



Particular, , 

Singular, . . , 

I Indefinite, . 



Pure, 

Modal. 

Conditional 

Disjunctive. 
i Affirmative, 
I Negative- 

True, 

False. 

reducible to 

Universal and 

Particular. 



SECTION II. 

OF THE MODALITY OF PROPOSITIONS. 

Modal propositions have been already cursorily noticed in 
the manner in which they are generally treated, viz., that of 
considering any proposition to be modal in which the copula 
is affected, by some modifying word, e. g. — 

Men are necessarily mortal. 



MANUAL OF LOGIC. 105 

A modal proposition of this description consists of what is 
termed the dictum and the modus. The dictum is the sub- 
ject, and the modus the predicate. In the examples given 
already, there is no difficulty in distinguishing the subject 
from the predicate, for they stand in their legitimate order, 
while the nature of their relation is determined by the word 
qualifying the copula; and the relation may be either that 
of necessity, possibility, impossibility, or contingency. But 
propositions often occur, usually considered modal, in which 
it is often requisite to alter the arrangement of the words in 
which they are expressed, in order to see clearly which is the 
dictum, and which the modus. In such cases, it is necessary 
first to ascertain the term, or the particular number of words 
constituting a term, which represents the dictum ; and when 
this is ascertained, all that remains is, to connect the term 
constituting the modus with the copula, — for the modus must 
be always joined to the copula, — and what is so joined is the 
predicate. In the following proposition, viz., 

It is necessary that a man should be an animal, 

there is a necessity of agreement asserted between the subject 
and predicate, and on examining the proposition, we find 'that 
a man should be an animal ' is the dictum or subject, and 
4 necessary ' the modus or predicate. By uniting the modus 
with the copula, the proposition will stand thus : 

That a man should be an animal is necessary. 

It is evident that the first kind of modal propositions men- 
tioned, (viz., those in which the subject and predicate occupy 
their legitimate places) may be multiplied to any extent ; for 
any adverb affecting the copula, and thereby qualifying the 
predicate, or even an adjective qualifying the subject, is suf- 
ficient to rank the proposition in which it occurs in this class 
of modals. It may be remarked, however, that this indefinite 
multiplication of modals is not to be attributed to Aristotle ; 

E 2 



106 MANUAL OF LOGIC. 

it originated with his Greek commentators, and was followed 
out by subsequent logicians. On the other hand, the various 
forms under which modal propositions of the latter description 
appear, although, as well as the former, easily reducible to the 
categorical form, will, if they are to be resolved into the dictum 
and modus, which they easily may be, constitute a second 
class of modals equally numerous. If, however, modality is 
to be restricted to one or both of these classes (and it would 
appear that these are the only kinds of it recognisable in pure 
logic, as they necessitate, under certain conditions, a corres- 
ponding modification of their immediate or mediate conse- 
quents), a little consideration will suffice to show, that the pro- 
positions falling under either of the classes should be designated 
propositions verbally modal — their modality being expressed, 
not implied; for in all cases, by a slight alteration in the 
phraseology, or a different arrangement of the order of the 
terms, they may be reduced to pure categorical proposi- 
tions. 

Whether modality, either expressed or implied in a propo- 
sition, should be relegated from the domain of pure logic, is a 
question among logicians. Some, holding the formal view, 
admit the expressed, but reject the implied; while others ex- 
clude both. No sufficient reason has been shown, however, 
why expressed modality should be banished from pure logic; 
for if a premiss is assumed under a necessity, or probability, 
or possibility, of being true, any of these conditions will, in a 
corresponding degree, determine the conclusion to be deduced, 
which, under any of these assumptions will be as purely logi- 
cal as that the truth of the conclusion follows from the truth 
of the premisses, or the falsity of the conclusion from the falsity 
of the premisses. 

In applied logic, on the other hand, there seems no reason 
why implied modality should not be recognised ; and hence 
the modality of a proposition would depend, in many cases, 
not on the effect a qualifying epithet may have on the copula, 



MANUAL OF LOGIC. 107 

but on the degree of certainty a thinker may entertain re- 
garding a judgment, and in contradistinction to verbal mo- 
dality, it might be very properly designated material modality. 
Aristotle, whose view of modality may be, with some strain- 
ing, interpreted either as expressed or understood in a pro- 
position, enumerates four modes, viz., the necessary (amyxcuov), 
the impossible (advvccrov), the contingent (svds^ofisvov), and the 
possible (dvvarov). "Whether he added the true (aX?j0sg) and 
the false (ova, aXriQec) is not quite clear. From his classifica- 
tion of judgments, however, and the grounds on which they 
must be explained, it may be presumed that he would not 
exclude implied modality from applied logic. In this view, 
therefore, the modality of a judgment in applied logic may 
depend on our knowledge of facts and things, or the degree 
of certainty with which we can assert the agreement or dis- 
agreement of any given subject and predicate. Hence the 
modality of our judgments will vary with the increase of our 
knowledge, and what is problematical at one time may 
amount to belief at another. The objective facts and things 
concerning which we judge remain the same, whatever 
changes may take place in the mind of the thinker as to 
clearer apprehensions of them. The change is subjective, not 
objective. 

On examining Aristotle's four modes, it will appear that all 
possible judgments may be reduced to three classes, viz., the 

Problematical, 
Assertory, and 
Demonstrable. 

This is Aristotle's distribution. All judgments which are 
merely matters of opinion come under the class ' problemati- 
cal;' all judgments founded on belief may be referred to the 
class 'assertory;' while all judgments resulting from the 
axioms and deductions of pure science belong to the class 
' demonstrable.' 



108 MANUAL OF LOGIC. 

Of the three, the problematical judgment is obviously the 
weakest, for it is neither regarded as true by the thinker, 
nor can it be shown to be a true decision in reference to the 
object or thing concerning which the judgment is made. 
Consequently, it cannot be laid down as truth either in a 
subjective or objective sense. In illustration, let us take the 
following example : — 

The solar system may be a gradual projection from the sun. 

In this judgment, there may be either a total, partial, or no 
agreement between the subject and predicate; but from our 
imperfect knowledge of the object-matter of the judgment, 
we can only affirm a possible dependence or agreement be- 
tween them. The judgment may indeed be true, and farther 
knowledge may prove it so, but now it is merely matter of 
opinion. 

All judgments which rest on possibility or probability, or 
to which doubt attaches in the mind of the thinking subject, 
may be classed under problematical judgments. 

The learner should observe, that in propositions the words 
' may be' often occur in two different senses. In the proposi- 
tion, The world may be circumnavigated, ' may be' means 
is capable of being, and the proposition is assertory ; while in 
the proposition, All the species in the world may be the off- 
spring of a few primary species, 'may be' means are, for 
anything we know, and the proposition is problematical. 

An assertory judgment implies belief in addition to opinion, 
and is therefore subjectively true, i. e., held as true by the 
thinker. An assertory judgment may also be true with re- 
spect to the fact or object regarding which it is made, but its 
truth objectively is indemonstrable. An assertory judgment 
is therefore subjectively true, but not objectively certain. 
The following is an example of an assertory judgment: — 

A mixed monarchy is the best form of government ; 



MANUAL OF LOGIC. ] 09 

and to a person holding this opinion as belief, the judgment 
is subjectively true, inasmuch as the thinking subject believes 
it to be so. Objectively, however, it is not certain, for one 
may believe the democratic, a second the despotic, and a 
third the patriarchal, to be the best form of government. An 
assertory differs from a demonstrable judgment in this, that 
however firm our own belief may be in the truth of an asser- 
tory judgment, we cannot compel men in general to acquiesce 
in it, because however strong the evidence in its favour may 
be, it cannot amount to absolute demonstration. 

Belief in the truth of an assertory judgment may be con- 
fined to one thinking subject, because he may have examined 
the object-matter of it more carefully and minutely than 
other thinking subjects, or he may have been influenced by 
prejudice, interest, or any other adequate cause. 

Belief in the truth of an assertory judgment may be com- 
mon to any particular sect or school, e. g., Calvinists may be- 
lieve in common that Calvin's Institutes are the best compend 
of Theology. The same holds true in the case of political 
classes, or in philosophical schools, &c. This coincidence of 
belief may arise from similarity in habits of thought, or from 
educational training, or any cause sufficient to present a judg- 
ment to the mind of the thinking subject as true. 

Belief in the truth of an assertory judgment may be com- 
mon to all, e.g., That there is a First Cause; That there is 
a day of final retribution; That there is a future state; are 
matters to which universal belief is acceded, although not 
susceptible of absolute demonstration. 

In every case, the truth of an assertory proposition, whe- 
ther held by an individual, or a class, or men in general, 
depends on moral not on demonstrable certainty. 

Belief in the truth of a demonstrable judgment occupies 
the highest place in the scale of credibility. It is not only 
subjectively, but also objectively true, and differs, conse- 
quently, both from the problematical and assertory judgment. 



110 MANUAL OP LOGIC. 

A demonstrable judgment is self-evident, as in mathematical 
axioms, e. g. — 

If equals be added to equals, the wholes are equal. 

Things which are equal to the same thing are equal to one 
another. 
Or it may be a deduction from self-evident principles; as, 

The circumference of a circle is thrice its diameter. 

The angles at the base of an isosceles triangle are equal. 



SECTION III. 

THE OPPOSITION OF PROPOSITIONS. 

Propositions have hitherto been treated in their absolute 
character, we now proceed to consider them in their relative 
character or affections. The relative affections of proposi- 
tions are of three kinds, viz., subalternation, conversion, and 
opposition. A knowledge of these is subservient to the doc- 
trine of syllogisms; for by subalternation we infer several 
conclusions from the same premisses ; by opposition we reduce 
imperfect moods to perfect, while conversion aids in both. 

1. Subalternation. 

Subalternation is the deduction of a particular or singular 
proposition from a universal, — both, namely, the premiss and 
deduction, having the same subject and the same predicate. 
Subalternation is either between A. and I. or E. and O. 

The two propositions compared together are — the one a 
universal proposition, called the subalternans ; the other, de- 
duced from the former, and called the subalterna, — a particu- 
lar or singular proposition, with the same subject and the 
Same predicate. In all cases the subalternans and subaltern a 
must agree in quality, e. g. — 

A. All diseases are contagious. 

I. Some diseases are contagious. 



MANUAL OF LOGIC. Ill 

The principle on which subalternation proceeds is, that 
universals include particulars, but that particulars do not 
include universals. 

From any universal proposition we may infer a particular 
subalterna; but before we can infer a singular subalterna, 
the subalternans must be metaphysically universal. The 
following is an example of a proposition metaphysically uni- 
versal; viz., 

Every effect has a cause ; 

and as it is metaphysically universal (that is, admitting of no 
exceptions), we can infer from it not only the particular 
proposition, 

Some effects have causes, 
but also the singular proposition — 
Gravitation has a cause. 

The relation between a subalternans and a subalterna can 
scarcely be called opposition, in the common acceptation of 
the term, though it comes within the range of the definition 
of that term as here used. 

In pronouncing on the truth or falsehood of propositions 
thus related, we have to consider how far we may infer the 
truth or falsehood of one of them from the truth or falsehood 
of the other ; and in reference to subalternation, we have the 
four following axioms : — 

1. The truth of the universal infers the truth of the par- 
ticular, — for if it be true that 

All islands are surrounded by water, 
it must be true that 

Some islands are surrounded by water ; 
and it is also true that 

Sicily is an island surrounded by water. 



112 MANUAL OF LOGIC. 

In this example, however, we infer a singular subalterna, 
because the subalternans is metaphysically universal. 

.A sign of universality prefixed to the subject of a proposi- 
tion does not, let it be observed, necessarily render that pro- 
position metaphysically true, e. g., the following proposition : — 

All children reverence their parents, 
is only morally universal, and therefore admits of some excep- 
tions; for all children do not reverence their parents; and hence, 
although from such a proposition we can infer with truth that 

Some children reverence their parents, 

we cannot infer this with regard to any particular individual 
contained in the subject ; for it may be among the exceptions. 

The truth of this axiom is equally valid in negative as 
,in affirmative propositions ; for if in affirmative propositions 
the predicate contains the whole extension of the subject, it 
contains a part ; and if in negative propositions it excludes 
the whole, it excludes a part. 

It will be seen from the foregoing, that the subalternans and 
the subalterna, deduced from it, differ in quantity but agree 
in quality. 

2. The truth of the particular does not infer the truth of the 
universal. 

The predicate of a proposition may agree with a part of 
the extension of the subject, yet it may not agree with the 
whole extension of the subject ; for although it may be true that 

Some wars are just, 
it is not true that 

All wars are just ; 
and although it may be true that 

Some men have not an affectionate disposition, 
it is not true that 

No men have an affectionate disposition. 



MANUAL OP LOGIC. 113 

In reference to the terms of a proposition, it is to be laid 
down that in any inference no term can be changed from a 
particular to an universal ; in other words, that an argument 
a particulari ad universale is invalid ; for if any term is 
particular, a part of it only is said to agree or disagree with 
the other term. About the remaining part of it, therefore, 
nothing can be inferred. 

3. The falsehood of the particular infers the falsehood of 
the universal. 

In illustration of this axiom, it may be stated that if it be 
false that the predicate contains or agrees with any part of 
the extension of the subject, it must also be false that it con- 
tains the whole ; for instance, if it is false that 

Some men are patriotic, 

it must be false that 

All men are patriotic. 

4. The falsehood of the universal does not infer the false- 
hood of the particular. 

It may be false, for instance, that the predicate contains or 
excludes the whole extension of the subject, yet it may con- 
tain or exclude a part. Thus it may be false that 

All men are logicians, 
or that 

No island is fertile ; 
yet it may be true that 

Some men are logicians, 
or that 

Some islands are not fertile. 

It must be observed, in relation to the four axioms, that we 



1 14 MANUAL OF LOGIC. 

are to understand by the universal and particular propositions 
mentioned, a universal and a particular deduced from it by 
subaltern ation. 

On examining the four foregoing axioms, it will appear 
that they may be reduced to two, for the third is contained in 
the first, and the fourth in the second. 

The third and fourth axioms differ from the first and 
second, in being their converses by contraposition. 

It may be mentioned that Aristotle takes no notice of sub- 
altern propositions. Its laws were first laid down by Apuleius, 
and the name given by Boethius. 

2. Contrary Opposition, 

Contrary Opposition is between two universal propositions 
differing in quality only, viz., between A. and E. ; as, 

All trees possess vegetable life. 
No trees possess vegetable life. 

With regard to the truth of contrary propositions, both of 
them may be false, but they cannot both be true, or the one 
may he false and the other true. 

When the opposed propositions are in necessary matter, 
the affirmative will be true and the negative false ; e. g. — 

A. All human institutions are imperfect. 
E. No human institutions are imperfect. 
A. All bad habits should be avoided. 
E. No bad habits should be avoided. 

When the opposed propositions are in impossible matter, 
the negative will be true and the affirmative false ; e. g. — 

E. None of the planets are stationary. 

A. All the planets are stationary. 

E. No island is under water. 

A. All islands are under water. 



MANUAL OF LOGIC. 115 

When the opposed propositions are in contingent matter, 
both are false; but the particulars, whether affirmative or 
negative, are both true. The following propositions — 

A. All children honour their parents, 
E. No children honour their parents, 

have the same terms ; and these are used in each of the pro- 
positions in exactly the same sense; yet both the propositions 
are false — for in contingent matter universals are false, and 
particulars true ; and all we can with truth assert is, that 

I. Some children honour their parents. 

0. Some children do not honour their parents. 

With respect to contrary propositions it appears, therefore, — 

1. That in necessary matter affirmatives are true, and ne- 
gatives false. 

2. That in impossible matter negatives are true, and affir- 
matives false ; and, 

3. That in contingent matter, both propositions are 
false. 



3. Sub-contrary Opposition. 

Sub-contrary Opposition subsists between two particular 
propositions differing in quality, viz., between Land O.; e.g. — 

Some minds are too much beclouded with prejudice to 
admit of the light of genuine science. 

Some minds are not too much beclouded with prejudice, 
to admit of the light of genuine science. 

Sub-contrary opposition has been so named, from the 
opposed propositions being under two universal contraries. 
Sub-contraries must have the same terms as the contraries 
to which they are related. 



1 1 6 MANUAL OF LOGIC. 

In necessary matter particular affirmatives are true, but 
particular negatives false ; e. g. — 

Some human institutions are imperfect. 
Some human institutions are not imperfect. 

In the former of these examples, the predicate agrees with 
the whole subject, and the proposition is consequently true; 
while, in the latter example, the predicate disagrees with the 
whole subject, and the proposition is consequently false. 

In impossible matter particular negatives are true, but par- 
ticular affirmatives false ; e. g. — 

Some of the planets are not stationary. 
Some of the planets are stationary. 

In the particular negative the predicate disagrees with the 
whole subject; and being in impossible matter, the proposi- 
tion is true. In the particular affirmative the predicate is 
asserted of the whole subject; but being in impossible matter, 
the proposition is false. 

In contingent matter sub- contrary propositions may both 
be true ; e. g. — 

Some men are astronomers. 
Some men are not astronomers. 

In the first of these examples the predicate is said to agree 
with part of the subject, and in the last the same predicate is 
said to disagree with part of the same subject. The predi- 
cate is therefore not really affirmed of the same subject, but 
of different parts of the same subject. Hence, both pro- 
positions are true. But between two sub-contrary proposi- 
tions, in contingent matter, there is in reality no opposition. 
Sub-contraries cannot be both false, nor can they be both 
true, except in contingent matter. The very definition of 
contingent matter requires that it should be such as to allow 
the predicate to be at the same time asserted of some things 
contained under the subject, and denied of others. 



MANUAL OF LOGIC. 117 

With regard to sub-contrary propositions, it is evident, 
therefore, 

1. That in necessary matter, affirmatives are true and 
negatives false. 

2. That in impossible matter, negatives are true and 
affirmatives false ; and, 

3. That in contingent matter, both the propositions are 
true. 

4. Contradictory Opposition. 

Contradictory Opposition is that which subsists between two 
propositions, differing both in quantity and quality, viz., be- 
tween A. and 0. or E. and I. ; e. g. — 

A. All men are responsible. 

0. Some men are not responsible. 

Of all the kinds of opposition, the contradictory is the 
most perfect ; for contradictories differ from each other in all 
points; in quantity, for one is universal and the other par- 
ticular; in quality, for one is affirmative and the other nega- 
tive. Hence it follows, that when a proposition is true, its 
contradictory must of necessity be false; and, conversely, if a 
proposition is false, its contradictory must be true. There 
can be no intermediate judgment. Consequently, contradic- 
tories can neither be both false nor both true together, for 
the falsity of the one establishes the truth of the other. 

In order that two propositions should be directly contra- 
dictory, the terms of both the propositions must be used in 
exactly the same sense with respect to each other. The con- 
ditions necessary to ensure this are the following, viz., that the 
terms of the contradictories must be used : — 

1. Eodem modo, in the same manner. 

2. Secundum idem, as to the same part. 

3. Ad idem, compared with the same thing. 

4. Eodem tempore, existing at the same time. 



118 MANUAL OF LOGIC. 

If any one of these conditions be omitted, is and is not may 
be compatible, e. g., an opinion is and is not faith ; it is a 
dead faith ; it is not living faith. 2. Zoilus is and is not 
black; for his face is black, and his hair is not black, but red. 
3. Socrates has and has not a full head of hair ; for he has, if 
compared with Scipio, he has not, if compared with Xeno- 
phon. 4. Nestor is and is not old ; for he is, if you speak of 
his third age, he is not, if you speak of his first. 

The four requisites to a complete contradiction may be 
comprised in one rule, which is equally applicable to all the 
species of opposition, viz., that the subject and predicate of 
the opposing propositions must be employed in the same sense 
and in the same manner with respect to each other. 

Let the opposing propositions be A. and O. in necessary 
matter, e. g. — 

A. All men are responsible. 

0. Some men are not responsible. 

In the universal affirmative the predicate l responsible ' is 
asserted universally of the subject ' men/ and in the negative 
proposition the same predicate, used exactly in the same 
sense, is denied partially of the same subject, used also exactly 
in the same sense ; but since the matter is necessary, the ex- 
tremes of the affirmative agree essentially, and the proposi- 
tion is consequently true; its contradictory, therefore, (the 
particular negative), which asserts the partial disagreement 
of the extremes, must be false. 

Let the opposing propositions be E. and I. in impossible 
matter, e. g. — 

E. No human institutions are perfect. 

1. Some human institutions are perfect. 

In the universal negative the predicate ' perfect ' is denied 
wholly of the subject 'human institutions,' and in the particular 
affirmative the same predicate, used exactly in the same 



MANUAL OF LOGIC. 119 

sense, is asserted partially of the same subject, used also 
exactly in the same sense ; but since the matter is impossible, 
the extremes of the negative disagree essentially, and the pro- 
position is consequently true ; its contradictory, therefore, (the 
particular affirmative), which affirms the partial agreement of 
the extremes, must be false. 

Let the opposing propositions be A. and O. in contingent 
matter, e. g — . 

A. All human inventions are beneficial to mankind. 

0. Some human inventions are not beneficial to mankind. 

In the universal affirmative, the predicate, ' beneficial to 
mankind,' is affirmed of the whole subject, ' human inven- 
tions ;' but on examining the matter, it will appear that the 
connection between the extremes is not invariable and essen- 
tial, and that all we can assert with truth is, that 

Some human inventions are beneficial to mankind. 

Hence there is a part of the subject with which the predicate 
does not agree ; and with respect to the part excluded, it may 
be asserted that 

Some human inventions are not beneficial to mankind. 
Hence the particular negative is true, and its contradictory, 
the universal affirmative, false. 

Let the quality of the above propositions be changed into 
E. and L, e. g. — 

E. No human institutions are beneficial to mankind. 

1. Some human institutions are beneficial to mankind. 
And from the preceding illustration, it will be seen that the 
particular affirmative is true, and its contradictory, the uni- 
versal negative, false. 

In the case of contradictory propositions, it appears, there- 
fore, — 

1. That in necessary matter, affirmatives are true and 
negatives false. 



120 MANUAL OF LOGIC. 

2. That in impossible matter, negatives are true and affir- 
matives false ; and, 

3. That in contingent matter, universal affirmatives are 
false, and particular negatives true, and that universal nega- 
tives are false and particular affirmatives true. 

5. Opposition of Singular Propositions. 

It is difficult to refer the opposition of singular propositions 
(sometimes called secondary contradiction) to any particular 
kind of opposition. Ostensibly their opposition is that of 
contrariety, for their quantity cannot be changed. 

The matter of singular propositions cannot be contingent ; 
and, consequently, two singular propositions cannot both be 
false, as may happen in the case of contraries, when they are 
both in contingent matter. The opposition of singulars is, 
therefore, not properly referrible to contrariety. 

Singular propositions must be either in necessary or im- 
possible matter ; and hence the contrary to a singular propo- 
sition forms as perfect an opposition as the contradiction 
between universals and particulars, for they have the essential 
features of contradictories, viz., that the one is always true 
and the other false ; for if a singular be true, its contrary 
must of necessity be false, and vice versa, since in necessary 
or impossible matter no two opposed propositions can be both 
true or both false together. 

[Note.] 

According to the formal view of logic, the words ' necessary,' 4 impossible,' 
' contingent,' should have no place in the doctrine of opposition ; for in order 
to carry out the formal view consistently, the logician can take no account of the 
material tru th or falsehood of a proposition. He has merely to do with the 
formal inferences or deductions which follow from the assumed truth or falsity 
of a premiss. It may be remarked, that, in reference to the doctrine of opposi- 
tion, the formal view may be easily maintained by expressing the canons or 
axioms hypothetically. 



MANUAL OF LOGIC. 



121 



The opposition of propositions is summarily presented in 
the annexed Scheme : — • 







A. 


I. 




'Between A & I....- 


N.— True. 
L— False. 


True. 
False. 






, C.— False. 


True. 


/Subaltern { 




E. 


0. 




v Between E & 0....- 


N.— False. 
I,— True. 


False. 
True. 




k C— False. 


True. 




A. 


E. 


Contrary Between A & E ....- 


N.— True. 
I.— False. 


False. 
True. 




,C.— False. 


False. 




r I, 


0. 




N.— True. 
I.— False. 


False. 
True. 




^C— True. 


True. 




( A * 


0. 




/ Between A & ...* 


N.— True. 
I.— False. 


False. 
True. 






C.— False. 


True. 


VContradictory, , 




E. 


I. 




\ Between E &I - 


N.— False. 

I.— True. 

.C— False. 


True. 
False. 
True. 



In the above Scheme the letters NIC denote the matter of the proposi- 
tions, viz., necessary, impossible, contingent. It has been preferred here to the 
scheme usually given in logical treatises, as more intelligible, and therefore 
more likely to secure attention. 

F 



122 MANUAL OF LOGIC. 



SECTION IV. 

OF THE CONVERSION OF PROPOSITIONS. 

Conversion is the transposition of the subject of a proposi 
tion into the place of the predicate, and of the predicate into 
the place of the subject; but in the transposition, both the 
quality and the truth of the proposition must be preserved.* 

The proposition to be converted is called the convertend or 
exposita, and that into which it is converted, the converse. 

In legitimate conversion, the truth of the converse ought 
to follow from the convertend, because logical conversion 
must be illative, that is, the truth of the convertend necessi- 
tates the truth of the converse. If, therefore, the convertend 
is true, its logical converse must also be true. 

Illative or inferential conversion is, when the truth of the 
converse may be intimated by the words ' therefore,' ' where- 
fore,' ' consequently,' &c. ; hence these are called illative par- 
ticles. But it should not be supposed, from the words ' illa- 
tive ' or ' inferential,' that this conversion is a process of 
reasoning, b — it is, in fact, only stating the same judgment in 
another form. 

a The terms of a logical proposition are the noun and verb ; the former as 
subject, the latter as predicate. In propositions tertii adjacentis, the copula 
and predicate are considered as equivalent to a single verb. When the terms 
are transposed, the noun must become a verb to form the new predicate, and 
the verb a noun to form a new subject. For this reason, all propositions should 
be resolved into the form tertii adjacentis before conversion, in order that the 
predicate may be freed from the con signification of time, so as to form a noun, 
and the copula may be left to unite with the subject, and form a verb. — Han- 
sel, p. 49. 

b Whether the converse is to be considered an inference is a question of some 
interest, from its having been a contested point among the scholastic commenta- 
tors of Aristotle at an early date. There can be no doubt that Aristotle himself 
considered it an inference, from the labour he expends in endeavouring to 



MANUAL OF LOGIC. 123 

Hence it follows, that no converse may assert, more ge- 
nerally, than the convertend, — in other words, a consequence 
must not go beyond its premisses, and, consequently, what is 
affirmed in the convertend of a part only, cannot, in the con- 
verse, be affirmed of the whole. When we attempt to deduce 
from a proposition another which does not necessarily follow, 
it is said that there is no vis consequential. 

Illative conversion is of three kinds, viz., simple conver- 
sion, conversion per accidens, and conversion by negation or 
contraposition. 

1 . — Simple Conversion, 

Simple conversion (gmtXtj avrisr^o<p7\) is the mere transposi- 
tion of the extremes of a proposition, without changing either 
the quantity or the quality. Hence, whether the convertend 
be universal or particular, affirmative or negative, the con- 
verse must retain the same attributes. 

In order that a proposition may be simply convertible, its 
extremes must be co- extensive, i. e-, both of them must be 

demonstrate it. Reid is of opinion, however, that his demonstration is merely 
arguing in a circle, and remarks that, ' it is indeed a fault very difficult to be 
avoided, when men attempt to prove things that are self-evident.' Reid, 
nevertheless, considers the converse to be an inference. The converse unquestion- 
ably depends entirely for its truth on the convertend ; but there is no reason why 
it should on that account be called an inference from it. Whateley's view is 
adopted in the text, only in reference to simple conversion ; for converses ob- 
tained in this way are obviously the same judgments in another form. This does 
not, however, in all cases hold true in accidental conversion, for here the con- 
verse or inference is not necessarily the same as the convertend or exposita. In 
simple conversion the converse must retain the accidental quality of the con- 
vertend ; the accidental converse, however, does not of necessity follow the truth 
of the convertend, except when the latter is true. Hence, if the convertend is 
false, its simple converse must also be false, but its accidental converse may 
be either true or false. Conversion per accidens is founded on the laws of sub- 
altern opposition, in which the particular does not retain the accidental quality 
of the universal unless the universal is itself true. 



124 MANUAL OF LOGIC. 

distributed, as is the case in universal negatives; or neither 
of them distributed, as is the case in particular affirmatives^ 
In either of these cases, the mere transposition of the extremes, 
without any alteration of the sign, does not interfere with the 
quantity, or the accidental quality (the truth or falsehood of 
the proposition). Hence, the only propositions which admit 
of simple conversion are universal negatives, and particular 
affirmatives, because in universal negatives both predicate 
and subject are universal terms, and therefore when transr 
posed the universal predicate of the convertend becomes a 
universal subject to the converse. In particular affirmations 
again, both predicate and subject are particular terms, and 
as the converse does not require any terms but particulars, 
they are sufficient to render it particular and affirmative. 

Of Universal Negatives. 

The following proposition, viz., 

No true philosophers omit the enforcement of moral duty, 

is simply convertible, for since both the terms are distributed, 
the proposition indicates that ' every true philosopher ' differs 
from ' every person who omits the enforcement of moral 
duty ;' while, on the other hand, it is equally true, that ' all 
who omit the enforcement of moral duty* differ from * all true 
philosophers,' consequently, the proposition may be simply 
converted thus — 

None who omit the enforcement of moral duty, are true 
philosophers. 

But to take a more obvious example, viz. — 
No angels are men. 

It is asserted in this proposition, that there is no individual 
common to the extension of both terms, for no individual in- 
cluded in the extension of the subject ' angels ' is included in 



MANUAL OF LOGIC. 125 

the extension of the predicate 'men;' and we may therefore 
affirm with certainty, that none of the individuals included in 
the extension of the predicate is found among the individuals 
included in the extension of the subject, — and consequently, 
the truth of the converse, viz., 

No men are angels, 

necessarily follows. 

Of Particular Affirmatives. 

Particular affirmatives are simply convertible, for since 
the extremes of the convertend are both particular, which is 
the case in all particular affirmatives, they retain their original 
quantity when transposed in the converse, e. g. — 

Some proud men occasionally stoop to acts of the basest 
servility. 

may be simply converted thus — 

Some who occasionally sloop to acts of the basest servility, 
are proud men. 

The truth of the simple converse of a particular affirma- 
tive is proved by Aldrich as follows: — If the particular affir- 
mative — Some blacks are civilised, is true, its contradictory, 
No blacks are civilised, is false, and so also is the simple 
converse of the contradictory, No civilised beings are blacks, 
therefore, the contradictory to this, viz., Some civilised beings 
are blacks, is true, which is the simple converse of the ori- 
ginal proposition, Some blacks are civilised. 

2. — Conversion per Accidens. 

Conversion per accidens, or, as it has been termed, con- 
version by restriction, or limitation, or particular conversion, 
is exemplified, when together, with transposing the extremes, 
of the proposition, the quantity is also changed ; in other 



126 MANUAL OF LOGIC. 

words, the quantity which is universal in the convertend is 
changed to particular in the converse, (the affirmation or 
negation of the original proposition being always, however, 
retained.) This kind of conversion may probably have been 
called per accidens* inasmuch as it is not a conversion of the 
universal per se, but rather as containing the particular. 
The propositions which admit of accidental conversion are 
universal affirmatives; and universal negatives. When the 
latter is accidentally converted, it is on the principle of sub- 
alternation, for it may be simply converted, as shown above. 

Universal Affirmatives. 

This class of propositions may obviously be converted per 
accidens; for from the truth of a universal affirmative a true 
subaltern necessarily follows, and as the subaltern is a par- 
ticular affirmative, it may be converted simply, and when 
so converted, it will be the accidental converse of the uni- 
versal affirmative. Thus, if it is true that 

Every poet is a man of genius, 
it is also true that 

Some poets are men of genius ; 
of which the simple converse must also be true, viz., that 

Some men of genius are poets, 

which is the accidental converse of the original proposition. 

For the sake of clearness, the three propositions may be 
brought together : — 

Original proposition,... Every poet is a man of genius. 

Subaltern, Some poets are men of genius. 

Accidental converse,. ..Some men of genius are poets. 

a Per accidens, putting in the place of the subject, the quality, whether 
proprium or accident, which the predicate implies. By the old logicians, the 
proprium is constantly called 'accidens proprium.' — Moberly, p. 85. 



MANUAL OF LOGIC. 127 

The reason why a universal affirmative cannot be con- 
verted simply, or into an universal affirmative, is, that in 
that case the predicate of the convertend would become the 
subject of the converse ; but since the predicates of affirma- 
tive propositions are particular, we would be arguing, did we 
convert such propositions simply, a particulari ad universale. 

There is a class of universal affirmatives, however, which 
may be simply converted, viz., reciprocal propositions. In 
such propositions the predicate is an adequate definition of 
the subject, as being co-extensive with it, e. g. — 

Wine is the juice of the grape ; 
simple converse — 

The juice of the grape is wine. 

All triangles are figures bounded by three straight lines ; 
simple converse — 

All figures bounded by three straight lines are triangles. 

Cicero was the discoverer of Catiline's conspiracy ; 
simple converse — 

The discoverer of Catiline's conspiracy was Cicero. 

The circumstances under which the subject and predicate 
reciprocate or change places with each other, without a 
change in signification, have been already explained. 

Mathematical propositions may be referred to this class, 
e.g.— 

All equilateral triangles are equiangular ; 

simple converse — 

All equiangular triangles are equilateral. 



128 MANUAL OF LOGIC. 

It is not necessary, however, to consider this last example, 
or its converse, as a universal proposition ; for we are not 
speaking of all triangles, but only of some triangles, viz., 
those which are equilateral ; we may therefore reduce it to a 
particular affirmative, and convert it simply as such, thus — 

Some triangles, i. e., all the equilateral, are all the equi- 
angular ; 

simple converse — 

Some triangles, i. e., all the equiangular, are all the equi- 
lateral. 

It may be remarked, that the accidental distribution of the 
predicate in affirmative propositions should not be allowed to 
affect an argument. An inference drawn from an accidental 
circumstance of this description would be illogical, for it sup- 
poses something to be known which is not made known by 
the premisses laid down. The inference would be correct in 
a material but not in a formal point of view. 

Universal Negatives, 

Universal negatives can be converted both simply and per 
accidens. For since the simple converse of a universal nega- 
tive is true, the subaltern deduced from that simple converse 
is also true ; thus, of the proposition, 

No larks are web-footed birds, 
the simple converse is, 

No web-footed birds are larks ; 
of which simple converse the subaltern is, 

Some web-footed birds are not larks ; 

and this is the converse per accidens of the original propo- 
sition. 



MANUAL OF LOGIC. 1 29 

Particular negatives cannot be converted either simply or 
per accidens ; for since the subject of a particular negative is 
not distributed, the converse would require the predicate to 
be undistributed, which is impossible in negative propositions, 
whether universal or particular. 

3. Conversion by Contraposition or Negation* 

Particular negatives, it has been said, cannot be converted 
either simply or per accidens, in the form of particular nega- 
tives, yet this class of propositions may be legitimately con- 
verted by shifting the sign of negation from the copula to 
the predicate, and thus rendering a particular negative a par- 
ticular affirmative, in which form it may be simply converted ; 
e. g., the proposition, 

Some animals are not rational, 

becomes affirmative by uniting the negative particle with the 
predicate, thus — 

Some animals are not-rational, or irrational ; 

which may be simply converted into, 

Some irrational beings are animals. 

The application of this mode of conversion to particular 
negatives has the same effect as if the particle of negation were 
disjoined from the copula and made a part of the predicate, 
and the proposition then simply converted like an affirmative. 

This mode of conversion may also be applied to universal 
affirmatives, in which, after transposing the terms, the nega- 
tive particle is combined with the new subject, and the 
proposition made negative by affixing the negative particle 



a This kind of conversion is not made any use of by Aristotle for logical 
purposes, although the principle may be gathered from his writings. It was 
first explained by Boethius. 

f2 



130 MANUAL OF LOGIC. 

to the copula, so as to form a contrary, viz., a universal nega- 
tive, which in signification will be found to be exactly equi- 
pollent to the original, for to assert the presence of some 
attribute is the same thing as to deny its absence ; e. g., the 
proposition, 

All poets are men of genius, 
by transposition and negation becomes, 

All not men of genius are not poets ; 
which is exactly equipollent to, 

No poets are not men of genius ; 
or, 

None but men of genius are poets. 

The following mnemonical lines may assist the learner in 
remembering the rules of conversion : — 

Simpliciter fEel, convertitur EvA per accid. 
AstO per contra, sic fit conversio tota. 

The two vowels in feci, E and I, represent universal 
negatives and particular affirmatives which are converted 
simply ; the two vowels in eva, E and A, denote universal 
negatives and universal affirmatives which are converted 
accidentally; and the two vowels in asto, A and O, indicate 
universal affirmatives and particular negatives which are 
converted by negation or contraposition. 



MANUAL OP LOGIC. 131 



CHAPTER IV. 



SECTION I. 



OF SYLLOGISM. 



Having already treated of simple apprehension and judg- 
ment, we now proceed to the third operation of the mind, 
viz., reasoning. 

In an act of reasoning, we compare two terms or concep- 
tions with some third term or conception ; and in this way 
ascertain whether any relation does or does not subsist 
between the two original terms or conceptions. A simple 
act of reasoning of this description is termed a syllogism. 

The term syllogism literally means a gathering or summing 
up ; and, as used in logic, it signifies a gathering of the con- 
clusion from the premisses. 

According to Aristotle, ' a syllogism is a speech a in which 
certain things (the premisses) being supposed, something dif- 
ferent from what is supposed (the conclusion) follows of 
necessity} 3 and this solely in virtue of the suppositions them- 
selves.' 

a The word \oyog here translated ' speech' might be rendered a sentence 
or thought, for Xoyog means either ratio or oratio, i. e., a thought, or a thought 
expressed. 

b The form or essence of a syllogism consists not in the truth of the judg- 
ment laid down, or that which is arrived at, but in the production of a new and 
distinct judgment, not a mere repetition of the antecedents, the truth of which 
cannot be denied without impugning those we have already accepted for true. 



132 MANUAL OF LOGIC. 

Aldrich defines a syllogism to be 'a speech in which 
certain things being laid down and granted, something else 
must follow distinct from but in virtue of those things which 
have been laid down and granted/ 

It has been shown, when treating of the relative affections 
of propositions, that one judgment may follow from another; 
but in these the terms of the new proposition are the same 
as those of the original proposition. There, from one propo- 
sition another was inferred, consisting of the same terms, 
either in the same order, as in subalternation, or in a trans- 
posed order, as in conversion. In a syllogism, however, 
there must be more than one proposition either expressed cr 
understood ; and the inference deduced, although following 
immediately from the premisses, must not consist of the same 
terms as any of the propositions from which it is deduced, e. g. — 

Every man is fallible. 
The Pope is a man. 
The Pope is fallible. 

It is plain, however, that the propositions forming the pre- 
misses must have a necessary connection with each other ; 
for if this were not the case, no conclusion could follow from 
them, e. g., from the propositions- 
Paul was the Apostle of the Gentiles, 
Rome was mistress of the world, 

no conclusion can be inferred, because no connection exists 
between them ; whereas, in fact, the connection between the 
premisses and the conclusion should be such, that from a 
knowledge of the former the mind should be led irresistibly 
to the latter. 

The premisses, whatever be their matter, should be laid 
down as hypothetical ly true, inasmuch as the principles from 
which the conclusion is drawn are supposed to be known and 
granted. 



MANUAL OF LOGIC. 133 

The connection existing between the premisses and con- 
clusion is termed in logic the consequence ; and of this there 
are two kinds, viz., the material and the formal. 9. 

The consequence is said to be material, when the conclu- 
sion follows from the premisses, in virtue of the matter of the 
argument, or the meaning necessarily attaching to the terms. 

The consequence is said to he formal, when the conclusion 
is inferred from the premisses, in virtue of the form of the 
expression. 

The formal consequence depends on the disposition of the 
terms, and cannot lead into error; but the material, as it 
depends solely on the meaning of the terms, may often lead 
to illogical conclusions. 

Every simple syllogism consists of three terms, and no 
more, viz., the subject, predicate, and middle term. 

Every syllogism consists of three propositions, viz., the 
major? and minor* premisses, and the conclusion* 

The major and minor propositions are by a common name 
called premisses, as they precede the conclusion. 

Every syllogism consists of two parts, viz., that which is 
proved, and that by means of which it is proved. That by 
means of which anything is proved is called the antecedent 
or premisses, and that which is proved is called the inference 
or conclusion. 

a Crakanthorpe explains the matter and form of syllogisms thus : — ' And as 
in a categorical proposition the two terms, namely, the subject and predicate, 
are the matter; the copula, on the other hand, which is the substantive verb, or 
some person of it, is the form; and as in a hypothetical proposition the two 
propositions are the matter, the conditional conjunction, copulative or disjunctive, 
which joins these propositions, is, as it were, its form. In like manner, also, 
in argumentation, the premisses and conclusion are its matter, and the illative 
mark, which unites them in the inference, is, as it were, the form.'' — [Book 3, 
cap. 13.] 

b t\ ir^oc, ru> /xs^ovi axgui irgoroxsig. 

c i] <7rgo$ ru) sXarrovi axgui ffgOTuaig. 

d (fv/xn-zgaGfia. — Aristotle. 



134 MANUAL OF LOGIC- 

The proposition proposed to be either proved or disproved 
is at first called the question (to fyrov/Mvov), and when the 
syllogism is formed, this proposition becomes the conclusion. 
Hence, in the phraseology of logicians, the question and con- 
clusion mean the same thing. 

The predicate of the question is called the major term 
(/x£/<^w!/ ogog), and its subject the minor term (sXarroov ogog), but 
in relation to the middle term, they are by a common name 
designated extremes. 

Any judgment, whether affirmative or negative, when ver- 
bally expressed, constitutes a proposition ; and as every pro- 
position must have a subject and predicate, the truth or falsity 
of the judgment enunciated by it depends on the agreement or 
disagreement of the terms representing the subject and pre- 
dicate ; and the nature of syllogistic reasoning is to prove the 
agreement or disagreement of these terms with some third 
term with which each of them is alternately compared in the 
premisses. This third term is by Aristotle called the middle 
term, not the argument, as usually stated. 

The three propositions of a syllogism are called its proxi- 
mate matter; and as they consist of three terms, these terms 
are called its remote matter. 

In every correct syllogism, the middle term occurs twice in 
the premisses, but never in the conclusion. 

The major term occurs in the major proposition ; and this 
proposition may be easily discovered by observing, that pre- 
miss which consists of the middle term, and the predicate of 
the conclusion. 

The major proposition is sometimes simply styled the pro- 
position. 

The minor term occurs in the minor proposition ; and this 
proposition may readily be distinguished by observing that 
premiss which consists of the middle term and the subject 
of the conclusion. 

The minor proposition is sometimes called the assumption. 



MANUAL OF LOGIC. 135 

The conclusion is designated variously the collection, in- 
ference, deduction, &c. 

The disposition of the terms of a syllogism will be best 
illustrated by an example. Let the question be, ( Is Chris- 
tianity worthy of belief?' 

Whatever is of divine origin is worthy of belief. 
Christianity is of divine origin. 
Christianity is worthy of belief. 

In this syllogism, ' worthy of belief,' i. e., the predi- 
cate of the conclusion, is the major term ' Christianity ;' its 
subject is the minor term, and 'of divine origin' is the 
middle term. 

The reason why the predicate of the conclusion is called 
the major term, and its subject the minor, is this, that the 
predicate of a universal affirmative proposition has gene- 
rally a greater extension than its subject, and must at least 
have as great, for a universal affirmative asserts that the 
entire extension of the subject is contained in the extension 
of the predicate ; and as a syllogism in which a universal 
affirmative conclusion can be deduced is deemed the most 
perfect kind, the extremes came to be invariably distinguished 
from each other by the names major and minor, on account 
of what is true of them when occurring in a universal affir- 
mative conclusion. 

The middle term in perfect syllogisms has a greater exten- 
sion than the minor, but not so great as the major; and 
hence it has received the name of middle. 

The reason why the major is called the proposition, and 
the minor the assumption, is, that when a syllogism is in its 
most perfect form, the major proposition is some generally 
admitted truth or principle, and therefore not likely to be 
called in question ; and for this reason it is, by way of emi- 
nence, sometimes called the proposition; while the minor 
proposition may be objected to as being an assumed truth, 



136 MANUAL OF LOGIC. 

having particular reference to the question under considera- 
tion ; and hence the name assumption, e. g., — 

Whatever acts with uniformity and consistency is the re- 
sult of intelligence. 

Nature acts with uniformity and consistency ; 

therefore, 

Nature is the result of intelligence. 

The major proposition in this example is a general truth 
which no one will call in question ; but the minor, viz., 

Nature acts with uniformity and consistency, 

is not a general truth, although accidentally it may be as well 
known. 

It is more convenient, but by no means necessary to the 
accuracy of a syllogism, that the major proposition should be 
first in order. In material arguments, it often happens that 
the minor premiss is first, and, still more frequently, that the 
conclusion begins the sentence. Thus — 

Habitual cheerfulness is the best promoter of health ; for it 
checks those secret anxieties and those violent ferments which 
derange and wear out the constitution ; and whatever has this 
excellent quality must have a tendency to promote health. 

In every syllogism the major proposition consists of the 
major and middle terms ; but whether the middle term is its 
subject or predicate depends on the figure of the syllogism. 

In like manner, the minor proposition in every syllogism 
consists of the minor and the middle terms ; but whether the 
middle term is its subject or predicate, depends also on the 
figure of the syllogism. 

By the figure of a syllogism is meant the legitimate dispo- 
sition of the middle term in the premisses ; and as the middle 
term may be either the subject or predicate of the major, or 



MANUAL OF LOGIC. 137 

the subject or predicate of the minor, it may be disposed in 
four different ways ; and, consequently, there are four figures. 
In the first figure the middle term is the subject of the 
major and the predicate of the minor, e. g. — 

Every philanthropist deserves to be held in remembrance. 

Howard was a philanthropist. 

Howard deserves to be held in remembrance. 

In the second figure the middle term is the predicate of 
both premisses, e. g. — 

The fixed stars do not revolve about a centre. 
The planets revolve about a centre. 
The planets are not fixed stars. 

In the third figure the middle term is the subject of both 
premisses, e. g. — 

Some acts of friendship are acts which militate against 
justice. 

All acts of friendship appear virtuous to the thoughtless. 

Some things which appear virtuous to the thoughtless 
militate against justice. 

In the fourth figure the middle term is the predicate of the 
major and the subject of the minor, e. g.— 

Some professors of the healing art are quacks. 
All quacks practice on the ignorance of the public. 
Some who practice on the ignorance of the public are pro- 
fessors of the healing art. 



138 MANUAL OF LOGIC. 



RULES OF SYLLOGISM. 



All the rules of syllogism are based on the three following 
canons, a viz., 

1. If any two terms agree with one and the same third 
term, they agree with each other. 

Let the question or problem be, ' Humility is worthy of 
constant cultivation.' The predicate, ' worthy of constant 
cultivation,' agrees with a third thing, viz., ' an ornament of 
the Christian character ;' but the subject, 'humility,' agrees 
with the same third ; therefore, the extremes agree with each 
other. Hence the following syllogism is correct : — 

Every ornament of the Christian character is worthy of 
constant cultivation. 

Humility is an ornament of the Christian character ; 

therefore, 

Humility is worthy of constant cultivation. 

2. If of two terms one agrees with the same third term, 
and the other disagrees with it, they disagree with each other. 

Let the question or problem be, ' Literature is not within 
the reach of the idle.' The subject, ' literature,' agrees with 
a third thing, viz., ' an acquisition of real value ;' but the pre- 
dicate, 'within reach of the idle,' differs from that third.. 

a The canons and special rules of syllogism given in Murray's Compendium 
are here adopted. Aldrich gives six canons and twelve rules, many of which 
are superfluous, from being included in the others. It may be proper to remark, 
regarding the three canons given, that although clear as principles in mathe 
matical reasoning, where they apply to equal magnitudes, they lose in some 
measure their definite meaning, when applied analogically to the agreement or 
disagreement of terms or conceptions in affirmative or negative propositions ; 
for the relation of the middle term to the major and minor, as to extension, 
varies according to the different figures ; and hence the comparison does not 
proceed on exact equality of quantities. 



MANUAL OF LOGIC. 139 

Therefore, the extremes disagree with each other ; and the 
argument is thus expressed — 

Acquisitions of real value are not within reach of the idle. 
Literature is an acquisition of real value. 
Literature is not within reach of the idle. 

3. Two terms, of which neither agrees with the same third 
term with which they are compared, may agree or disagree 
with each other. 

The agreement or disagreement of any two terms can only 
be ascertained by comparing each of them alternately with 
some one third term ; but it may happen that no third term 
can be found with which to compare them, so as to discover 
whether both agree with it, or the one agree with it and the 
other differ from it ; and therefore we cannot prove whether 
they agree with or differ from each other ; for since no third 
term has been brought forward with which to compare them, 
it is matter of doubt whether any such third term can be ad- 
duced. And hence their agreement or disagreement cannot 
be established until this doubt is removed. 

The use of a third term, in syllogistic argument, is indis- 
pensable ; for no syllogistic argument can exist unless there 
be a comparison of some two terms with a third, on one or 
other of the principles contained in the first and second canons. 

Those two canons may be considered as axioms, since they 
challenge immediate assent as soon as understood, and are the 
basis on which the syllogism is founded. They bear some 
analogy to the mathematical axioms : — Things which are equal 
to the same are equal to one another, and things of which 
one is equal and the other not equal to the same, are not 
equal to one another. 

The validity of all affirmative conclusions depends on the 
first of these canons, and the validity of all negative conclu- 
sions on the second. When the condition mentioned in the 
third canon is present, there can be no conclusion. 



140 MANUAL OF LOGIC. 

These two canons are closely allied to the Dictum* de omni 
(■/tara xavrog) and the Dictum de nullo (x,ara (iqdsvog), viz., 
that whatever is affirmed or denied of a whole class may be 
affirmed or denied of whatever is comprehended in that class. 
It is from conforming to these dicta that all syllogisms drawn 
in the first figure derive their validity ; for whatever can be 
predicated of a whole subject or class is necessarily a predi- 
cate of all the subjects, whether particular or singular, con- 
tained in that subject; and, on the other hand, whatever 
predicate can be denied of a whole subject or class is neces- 
sarily denied of all the subjects, whether particular or singular, 
contained under that subject. 

The rules of syllogism are of two kinds, viz., general and 
special. 

The general rules apply to all syllogisms, in whatever 
figures they may be drawn. The special rules, again, have 
reference to particular figures. 

The general rules are six : — 

1. The middle term cannot be taken twice particularly in 
the premisses, but must be at least once universal, i. e., by 
being the subject of a universal, or the predicate of a nega- 
tive proposition. 

It is plain, that if the middle term be twice particular, it 
can in either premiss represent only a part of its significates, 
and may therefore be taken for different parts of the same 
universal whole, and then there will be in reality two middle 
terms ; but it is with the same third term, and not with dif- 
ferent parts of it, that the other terms must be compared. 
If, then, the middle term is not distributed in one or other of 
the propositions forming the premisses, the major and minor 

a The dictum de omni et de nullo applies only to the first figure. The dicta 
applicable to the other figures are explained by Keckerman and Lambert, and 
will be noticed in their proper places. 



MANUAL OF LOGIC. 141 

terms will each be compared with only a part of it ; and we 
cannot know that this may have been the same part. Hence 
one of the terras may have been compared with one part of 
the middle term, and the other with another part of it, e. g. — 

Some arts are useful. 
Logic is an art. 
Logic is useful. 

In this example, the middle term is twice particular; for in 
the major proposition there is a sign of particularity prefixed 
to it ; and in the minor it is the predicate of an affirmative 
proposition. In the major proposition, therefore, the term 
'useful' is only compared with a part of the middle term 'arts,' 
and in the minor proposition the term 'logic' may be compared 
with another part of the middle term. But since from the 
form of the expression we cannot assert that both the ex- 
tremes have been compared with one and the same middle 
term, we cannot legitimately infer the conclusion, ' logic is 
useful,' but from such premisses as the following, viz., — 

All arts are useful. 
Logic is an art. 

We can legitimately infer the conclusion — 
Logic is useful. 

2. The extremes cannot be taken more universally in the 
conclusion than in the premisses. 

This rule may be more clearly understood by the explana- 
tion, that a term must not be distributed in the conclusion 
which was not distributed in the premisses. The object of the 
rule is to guard against inferring a universal conclusion from 
particular premisses. When either the major or minor term 
is employed universally in the conclusion, but particularly 
in the premisses, this is termed an illicit process of the 
major or minor term. A term undistributed in the pre- 



142 MANUAL OF LOGIC. 

misses, and the same distributed in the conclusion, cannot be 
called one and the same term ; and, consequently, to draw an 
inference from any term employed 'particularly to the same 
term employed universally is the same as to infer the truth of 
the universal from the truth of the particular ; for a term dis- 
tributed bears the same proportion to the same undistributed 
as a universal does to its particular, e. g. — 

All innocent things are allowable. 
Some pleasures are not innocent. 
Some pleasures are not allowable. 

In this example the major term 'allowable' is illicitly distri- 
buted, for it is particular in the major premiss, being the pre- 
dicate of an affirmative proposition ; but it is universal in the 
conclusion, being the predicate of a negative proposition. 
There are consequently two major terms, instead of one, and 
therefore four terms in the syllogism. The conclusion may 
be true notwithstanding, but its truth cannot be formally in- 
ferred from the premisses. 

In the following example, viz., 

All beasts of prey are carnivorous. 
All beasts of prey are animals. 
All animals are carnivorous, 

there is an illicit process of the minor term for the predicate 
of the minor proposition, ' animals ' is used particularly in that 
proposition, but universally in the conclusion ; consequently, 
the inference is illegitimate. 

It is evident, from the two preceding rules, that the num- 
ber of universal terms in the premisses must be at least one 
more than in the conclusion ; for by the second rule every 
term that is universal in the conclusion must be also universal 
in the premisses; but besides this, by the first rule, the 
middle term, which never enters the conclusion, must be at 
least once universal in the premisses. Therefore, there must 



MANUAL OF LOGIC. 143 

at least be one universal term in the premisses more than in 
the conclusion. 

It follows, that the number of universal terms in the pre- 
misses cannot exceed the number in the conclusion by more 
than two. For there can be but three universal terms in the 
premisses, as one of them, by the third rule, must be affirma- 
tive, and to afford three one of the premisses must be nega- 
tive. But in this case the conclusion must be negative by the 
fifth rule, and will therefore have its predicate universal. 
And that the excess may be two, the premisses should be E 
and A, and the conclusion O, or, if the mood be affirmative, 
the premisses must be A and A, and the conclusion I, in 
order to preserve the required excess. 

It follows, also, that the greatest number of particular 
terms that can occur in the premisses are three, when both 
are affirmative and one particular; and then the universal 
term that occurs in the premisses must be the middle term ; 
and therefore there are two particular terms in the conclusion. 
If there are but two particular terms in the premisses, both 
are affirmative, or one particular ; and so in either case the 
conclusion has a particular term. The excess is never more 
than one. 

3. From two negative premisses nothing follows. 

In this case a middle term is employed, from which both 
extremes differ ; and, consequently, there can be no inference, 
e. g. — 

No irrational being is accountable. 
Man is not an irrational being. 

Here the disagreement of the extremes with the middle term 
affords no ground for inferring that they either agree with or 
differ from each other. They may agree or differ ; but these 
premisses will neither prove their agreement or disagreement. 

4. From two affirmative premisses a negative conclusion 
cannot follow. 



144 MANUAL OF LOGIC. 

It must be assumed, in reference to this rule, that the pre- 
misses are not both particular ; for in that case, as shown 
below, there could be uo inference, and that there are not 
two middle terms ; for in that case, there could be no legi- 
timate conclusion, as has been explained above. If, ther&r 
fore, there be but one middle term, and the extremes agree 
with it, and consequently with each other, the conclusion 
must be affirmative, e. g. — 

Every science that tends to elevate our conceptions of the 
Deity is worthy of being studied ; 

Astronomy is a science tending to elevate our conceptions 
of the Deity ; therefore, 

Astronomy is worthy of being studied. 

5. The conclusion follows the weaker part. 

In logic a negative proposition is considered inferior to an 
affirmative, or weaker than it, and a particular weaker than 
a universal. 

This rule may be divided into two parts: — 

Part 1. — If one of the premisses be negative, the conclu- 
sion, as it follows the weaker part, will be negative also ; for 
in this case one of the extremes agrees with the middle term, 
and the other disagrees with it, and by the second canon 
they consequently disagree with each other, and the conclu- 
sion is negative. 

The premisses necessary to prove a negative conclusion are 
an affirmative and a negative, since the extremes can be 
shown to differ only by means of a middle term which agrees 
with the one and differs from the other, e. g. — 

No mere man is infallible. 

The Pope is but a mere man. 

The Pope is not infallible. 

Part 2. — If one of the premisses be particular, the conclu- 
sion will be particular, e. g. — 

All flowers are beautiful. 



MANUAL OF LOGIC. 145 

Some deciduous plants are flowers. 
Some deciduous plants are beautiful. 

In this example there are three particular terms in the 
premisses, viz., the two predicates, and the subject of the 
particular proposition ; consequently, there is but one uni- 
versal term in the premisses, viz., the subject of the major 
proposition ; and hence there can be no universal term in the 
conclusion, since the premisses must contain, at least, one 
more universal term than the conclusion. Hence the subject 
of the conclusion must be particular, and therefore the con- 
clusion itself. 

Again, if one of the premisses be negative, let them be A 
and O, e. g. — 

Every man is an animal. 

Some living things are not animals. 

Some living things are not men. 

In this example there are two particular terms in the pre- 
misses, viz., the predicate of the major proposition, and the 
subject of the minor ; therefore, there are but two universal 
terms, viz., the subject of the major proposition and the pre- 
dicate of the minor, and consequently, but one in the conclu- 
sion, which must be its predicate, as the conclusion is nega- 
tive. Hence the subject of the conclusion is particular, and 
therefore the conclusion itself. 

Again, if the premisses are not A and O, they must be 
E and I, e. g. — 

No works of human invention are perfect. 
Some machines are works of human invention. 
Some machines are not perfect. 

In this example there are also two particular terms in the 
premisses, viz., the subject and predicate of the minor ; there- 
fore, there are but two universal terms, viz., the subject and 

o 



146 MANUAL OF LOGIC. 

predicate of the major proposition, and consequently, but one 
in the conclusion, which must be its predicate. Hence the 
subject of the conclusion is particular, and therefore the con- 
clusion itself. 

6. From two particular premisses nothing follows. 

If both propositions be affirmative, there will be no uni- 
versal term in the premisses, and consequently, the middle 
term will be twice particular, e. g. — 

Some sciences are worth knowing. 
Some arts are worth knowing. 
Some arts are sciences. 

In this example the middle term is not distributed in either 
premiss, and consequently, no legitimate conclusion can be 
inferred. 

If, again, one of the premisses be affirmative, and the other 
negative, there will be but one universal term, viz., the pre- 
dicate of the negative proposition, and if a conclusion follow, 
it will be negative, and therefore its predicate universal ; con- 
sequently, there will be as many universal terms in the con- 
clusion as in the premisses, e. g. — 

Some talented men are not good men of business. 
Some Englishmen are good men of business. 
Some Englishmen are not talented men. 

In this example there is an illicit process of the major 
term ; for while it is used particularly in the premiss, it is 
employed universally in the conclusion, being the predicate of 
a negative proposition. 

Universal premisses do not always warrant a universal 
conclusion ; but when a universal conclusion can be drawn, 
it is allowable to deduce a particular, for the truth of the 
particular is implied in that of the universal. 

In testing the correctness of a syllogism by the foregoing 
general rules, we must see — 



MANUAL OF LOGIC. 147 

1. That the middle term has been distributed. 

2. That no term has been employed more universally in 
the conclusion than in the premisses. 

3. That both the premisses are not negative. 

4. That a negative conclusion is not inferred from affirma- 
tive premisses. 

5. That if one of the premisses be particular, the conclu- 
sion must be particular ; and that if one of the premisses be 
negative, the conclusion must be negative. 

6. That from two particular premisses no conclusion can 
be inferred ; and, 

7. That the conclusion is not particular where a universal 
may be inferred. 

SPECIAL RULES OF SYLLOGISM. 

First Figure. 
The special rules of the first figure are two : — 

1. The minor must be affirmative. 

2. The major must be universal. 

The special rules of syllogisms are founded on the prin- 
ciples implied in each figure. In the first figure the argument 
is from a general to a specific statement ; and hence we infer 
an attribute to belong, or not to belong to something, because 
it belongs or does not belong to a class in which that thing is 
contained. But in order to advance a general statement, the 
major must be universal, while the specific statement can 
only be inferred from it by means of an affirmative minor.* 

* The use of an argument in this figure implies that we possess (or conceive 
ourselves to possess) all required knowledge about both the subject and the 
predicate, which are the terms of our reasoning. The major premiss is a meta- 
physical proposition, ascribing a distinct predicate, whether proprium or acci- 
dent to a known genus or higher kind ; the minor premiss is a logical proposi- 
tion, including in this genus a known species or lower kind. The former 
premiss implies a sufficiently complete act of logical definition; the latter 
a sufficieLtly complete act of logical division. — Moberly, p. 100. 



148 MANUAL OF LOGIC, 

In syllogisms drawn in the first figure, the middle term, or 
medium of proof, is less extensive than the major, and more 
extensive than the minor. 

The middle term is the subject of the major proposition, 
and the predicate of the minor, e. g. — 

All luminous bodies emit particles of light. 
The sun is a luminous body. 
The sun emits particles of light. 

1. Of the Minor Projyosition. 

If the minor be negative, the major will be affirmative by 
the third general rule, and its predicate therefore particular, 
while the conclusion will be negative by the fifth general 
rule, and its predicate universal ; but in the first figure the 
major proposition and the conclusion have the same predi- 
cate, viz., the major term. The major term would therefore 
be particular in the major proposition, and universal in the 
conclusion ; but by the second general rule, a term cannot be 
employed more universally in the conclusion than in the pre- 
misses ; for this would be arguing a particulari ad universale. 
The minor must therefore be affirmative. 

2. Of the Major Proposition. 

Since the minor must be affirmative, the major proposition 
must be universal ; for if the major proposition is particular, 
the middle term, which is its subject, will also be particular; 
but since the minor must be affirmative, the middle term, 
which is its predicate, will be particular in it also ; the middle 
term will therefore be taken twice particularly contrary to 
the first general rule, and any inference drawn will be invalid. 
The middle term must therefore be distributed in the major 
premiss, in which by the first figure it is the subject, and 
universals alone distribute their subject. Any syllogism then, 



MANUAL OF LOGIC. 149 

in the first figure, will be inconclusive in which the minor is 
negative or the major particular. 

In the first figure, 

The major may be A or E. 

The minor may be A or I. 

The conclusion may be A, I, E, or O. 

Second Figure. 

The special rules of the second figure are two : — 

1. One or other of the premisses (and therefore the con- 
clusion) must be negative. 

2. The major must be universal. 

In the second figure the middle term is the predicate of 
both premisses, e. g. — 

No honest reasoner resorts to sophistical arguments. 
Some sectaries resort to sophistical arguments. 
Some sectaries are not honest reasoners. 

In syllogisms drawn in the second figure, the middle term 
or medium of proof is more extensive than either the major 
or minor term. 

The principle a of this figure is to prove a distinction or 
disagreement between two classes, or between one class and 
a portion of another, by showing that an attribute possessed 
by the one is wholly excluded by the other ; for if one term 

a The distinctive principles of this and the two following figures are 
founded on the conclusions arrived at by Lambert. Thb second figure is suited 
to the discovery or proof of distinctions between things, and its principle is 
called the dictum de diverso. The third figure is suited to the discovery or 
proof of instances and exceptions. Its principle is termed the dictum de exemplo. 
The fourth figure is suited to the discovery or exclusion of the different species 
of a genus. Its principle is designated the dictum de reciproco. The invention 
of these dicta, though generally attributed to Lambert, properly belongs to 
Keckerman, who published them about a century earlier. Lambert may, how- 
ever, claim the invention of the dictum of the fourth, as this figure was rejected 
by Keckerman. 



150 MANUAL OF LOGIC. 

is contained in, and another excluded from, a third term, they 
are mutually excluded. For this reason, the leading pro- 
position of the antecedent must be universal, and one of the 
premisses negative, e. g. — 

Every planet describes an orbit. 
The sun does not describe an orbit. 
The sun is not a planet. 

No planet is fixed. 
Every star is fixed. 
No star is a planet. 

Of the Negative Premiss. 

In the second figure the middle term is the predicate of 
both premisses ; and hence, if both the premisses are affirma- 
tive, the middle term will be particular in each, contrary to 
the first general rule. In the second figure, therefore, a cor- 
rect affirmative conclusion can in no case be drawn. 

Of the Major Premiss. 

It will be seen, from what has been said above, that one of 
the premisses must be negative, and consequently, the con- 
clusion ; but the predicate of the conclusion is universal, 
being the predicate of a negative proposition, and by the 
second general rule, it must be universal also in the major 
proposition, where it is the subject. The major premiss must 
therefore be universal in this figure; and any syllogism 
drawn in it, in which both the premisses are affirmative, or 
the major particular, will be illegitimate. . 

In the second figure, 

The major may be A or E. 

The minor may be E, 0, A, or I. 

The conclusion may be E or O. 



MANUAL OF LOGIC. 151 

Third Figure. 

The special rules of the third figure are two : — 

1. The minor must be affirmative. 

2. The conclusion must be particular. 

In the third figure the middle term is the subject of both 
premisses, e. g. — 

All men of wit are desirable companions. 

Some men of wit are indolent. 

Some indolent men are desirable companions. 

The principles of the third figure are two : — 1. If two 
attributes belong to the same class, or the same part of the 
same class, they may co-exist in the same class or subject. 
Hence the subjects will partly agree, the attributes not being 
incompatible or opposed to each other ; but in this case the 
conclusion must be particular, e. g. — 

All men are responsible. 

All men are mortal. 

Some mortal beings are responsible. 

For if ' responsibility ' and ' mortality' are both predicable 
of the species ' man,' as asserted in the premisses, it must 
follow that ' some mortal beings are responsible.' 

2. If of two attributes one belongs to a certain class, 
and the other is excluded from the same class, or the same 
part, the attributes do not universally co-exist in the same 
subject ; and in this case also, the conclusion must be par- 
ticular, e. g. — 

Some men are not virtuous. 

All men are responsible. 

Some responsible beings are not virtuous. 

For since the attribute * virtue ' is excluded from some men, 
and the attribute ' responsibility ' is predicable of all men, 



152 MANUAL OF LOGIC. 

the attribute ' virtue ' is separable from the attribute ' respon- 
sibility ;' and hence it follows, as a particular conclusion, that 
some responsible beings are not virtuous. 

In syllogisms drawn in this figure, the middle term or 
medium of proof is less extensive than either the major or 
minor term. 

The minor must be affirmative. 

If the minor is negative, the major will be affirmative, by 
the third general rule, and then its predicate will be par- 
ticular ; but in this case the conclusion would be negative, 
and its predicate, the major term, would be universal in the 
conclusion, and particular in the major proposition, where it 
is also the predicate, contrary to the second general rule ; but 
this has been shown, when explaining the same special rule, 
in the first figure. 

The conclusion must he particular. 

Since the minor proposition must be affirmative, as shown 
above, the minor term, as its predicate, is particular in it ; 
and as no term can be used more universally in the conclu- 
sion than in the premisses, it must be particular in the con- 
clusion also, where it is the subject; and consequently the 
conclusion itself must be particular. Hence any syllogism in 
the third figure will be illegitimate in which the minor is 
negative or the conclusion universal. 

In the third figure, 

The major may be A, E, I, or O. 

The minor may be A or I. 

The conclusion may be I or O. 

Fourth Figure. 

The special rules of the fourth figure are three : — 

1. If the major be affirmative, the minor must be universal. 

2. If the minor be affirmative, the conclusion must be par- 
ticular. 



MANUAL OF LOGIC. 153 

3. In negative moods (i. e., if any proposition be negative) 
the major must be universal. 

In the fourth figure the middle term is the predicate of the 
major proposition, and the subject of the minor, e. g. — 

All wise statesmen legislate with caution. 

All who legislate with caution regard the interests of the 
community. 

Some who regard the interests of the community are wise 
statesmen. 

The peculiar principle of the fourth figure is this : — If the 
whole or part of a class is contained in another, and that also 
in a third, then the first class must contain some individuals 
belonging to the third. If, again, one class universally ex- 
cludes another, which is in whole or in part contained in a 
third, the first is in part excluded from the third. But, on the 
other hand, if one class is universally contained under an- 
other, from which a third is wholly excluded, the third is 
wholly excluded from the first. Hence there cannot be a 
universal affirmative conclusion. 

Illustration of the rules : — 

1. If the major be affirmative, the minor must be uni- 
versal, e. g. — 

Worldly honours are transient vanities. 
All transient vanities are sources of certain disappoint- 
ment. 

Some sources of certain disappointment are worldly honours. 



In this example the major is affirmative, and its predicate, 
the middle term, therefore particular ; but the middle term is 
also the subject of the minor ; and if the minor were par- 
ticular, its subject would be particular ; and in this case the 
middle term would not be at all distributed in the premisses. 
The minor must therefore be universal, in order that its sub- 
ject, the middle term, may be universal. 

g2 






154 MANUAL OF LOGIC. 

2. If the minor be affirmative, the conclusion m.ust be 
particular, e. g. — 

Some learned men are egotistical. 

All egotistical men are fond of popularity. 

Some persons fond of popularity are learned men. 

In this example the minor is affirmative, and the conclu- 
sion must therefore be particular; for since the minor is 
affirmative, its predicate is particular ; but the predicate of 
the minor proposition is the same as the minor term or sub- 
ject of the conclusion ; the subject of the conclusion must 
therefore be particular, and therefore the conclusion itself. 

3. In negative moods the major must be universal, e. g. — 

No fallacious arguments are legitimate means of persuasion. 
Some legitimate means of persuasion fail in convincing. 
Some things which fail in convincing are not fallacious 
arguments. 

If either of the premisses be negative, the major must be 
universal, else the major term, which is the subject of the 
major proposition, would be particular ; but the subject of 
the major proposition, and the predicate of the conclusion, 
are the same ; and as the conclusion is negative, its predicate 
will be universal. The major term must therefore be uni- 
versal in the major proposition ; otherwise the inference would 
be a particulari ad universale. 

It is obvious, therefore, that any syllogism in the fourth 
figure will be illegitimate — 1. If the major be affirmative, and 
the minor particular ; 2. If the minor be affirmative, and the 
conclusion universal ; and, 3. If the conclusion be negative, 
r.n.l the major particular. 

In the fourth figure, 

The major may be A, E, or I. 

The minor may be A, E, or I. 

The conclusion may be E, I, or 0. 



MANUAL OF LOGIC. 155 

The fourth figure, introduced here merely to show all the 
possible ways in which the middle term can be arranged in 
the premisses, is not of Aristotelic origin. a It is attributed 
to Galen (hence called the Galenic figure) on the authority 
of Averrde's; but the words of Averrde's — viz., Et ex hoc 
planum, quod figura quarta, de qua meminit Galenus, non 
est syllogismus super quern cadet naturaliter cogitatio — are by 
no means decisive on the point. Aldrich truly says that this 
figure is nugatory, as it proves the middle term by itself. 
This we shall illustrate by the following example and analysis 
from Hill's notes on the Compendium, viz. — 

All metaphysical inquiries are involved in some degree of 
obscurity ; 

But all things involved in obscurity are liable to error ; 
therefore, 

Some things liable to error are metaphysical inquiries. 

This syllogism predicates the medium ' involved in obscu- 
rity' of the major term 'metaphysical inquiries;' this is 
predicated, in the conclusion, of the minor term, ' things 
liable to error;' and this minor term is predicated in the 
minor premiss of the medium, ' involved in obscurity ' — that 
is, the class of ' things involved in obscurity' is represented 
to comprehend all ' metaphysical inquiries ;' the term ' meta- 
physical inquiries ' is asserted to comprehend ' some things 
liable to error,' and l some things liable to error ' are repre- 
sented to comprehend ' everything that is involved in ob- 
scurity.' Thus it is implied in a circle, that * things involved 
in obscurity ' comprehend ' things involved in obscurity,' 
which is nugatory. 

a Aristotle acknowledges only three figures, and regards the middle term, in 
reference to its extension, as compared with the major and minor, rather than 
with reference to its position in the premisses. 



156 



MANUAL OF LOGIC. 



The following table presents at one view the special rules 
of the figures, with their respective proofs : — 



Fig. 


RULES. 


i 
PROOFS. 


1 


Minor premiss affirmative... 


Else illicit process of the major term. 




Major universal 


Else middle not distributed. 

1 


2 


One premiss negative 


Else middle not distributed. 






Because of the negative premiss. 
Else illicit process of the major term. 




Major universal 


3 


Minor affirmative 


Else illicit process of the major term, j 
Else illicit process of the minor term. 




Conclusion particular 


4 


Major premiss not 


Else illicit process of the major term. 




Minor premiss not 


Else middle not distributed. 




Conclusion not A 


Else illicit process of the minor term. 





The following table represents the propositions according 
to the quantity and essential quality which are admissible in 
each figure : — 



Fig. 


Major Proposition. 


Minor Proposition. 


Conclusion. 


1 
2 
3 
4 


Universal 

Universal* 

Any 

Any except 


Affirmative 

Any 

Affirmative 

Any except 


Any. 
Negative. 
Particular. 
Any except A. 



* In the second figure one premiss is negative. 



/ 



MANUAL OF LOGIC. 157 



The Moods of Syllogism. 

The mood of a syllogism is defined by Aldrich to be, Legi- 
tima determinate propositionum secundum quantitatem et 
qualitatem, i. e., the legitimate determination of the pro- 
positions with respect to quantity and quality. 

When, therefore, the three propositions of a syllogism are 
laid down in their proper order, as to their quantity and 
quality, the mood of the syllogism is determined. 

Vicious and illegitimate moods are of course excluded from 
the class of syllogisms to which the above definition applies. 
Vicious moods are designated paralogisms. 

Any three propositions in combination form a mood ; and 
as there are, in all, four kinds of propositions, and as each of 
these four kinds may be used as a major premiss, while each 
of these major premisses admits of four different minors, viz,, 
A, E, I, or O, there may be formed four times four, or six- 
teen pairs of premisses ; and to. each of these premisses may 
be subjoined a fourfold conclusion, viz., A, E, I, or O ; con- 
sequently, all the permutations that can possibly be formed 
amount to sixty-four. 

Of these sixty- four varieties, eleven only are found to be 
legitimate moods of syllogism. Consequently, fifty-three are 
excluded as violating some of the general rules, and are there- 
fore paralogisms. 

These permutations are of course nothing more than an 
arithmetical calculation, for the number of combinations that 
can be formed by any four things, taken three and three toge- 
ther, is 4 X 4 X 4 = 64. 

Of these, sixteen, viz., EEA, EEE, EEI, EEO, EOA, EOE, 
EOI, EOO, OEA, OEE, OEI, OEO, OOA, OOE, OOI, 
000, are excluded by the third general rule, because their 
premisses are negative. 

Twelve, viz., IIA, HE, III, 110, 10 A, TOE, I0I,I00,0IA, 



1 58 MANUAL OF LOGIC. 

OIE, Oil, OIO, are excluded by the sixth general rule, 
because their premisses are particular. 

Twelve, viz., AEA, AEI, AOA, AOI, EAA, EAI, EIA, 
EII, IEA, IEI, OAA, OAI, are excluded by the fifth gene- 
ral rule, because one of the premisses is negative, but not the 
conclusion. 

Eight, viz., AIA, AIE, AOE, EIE, I A A, IAE, 
IEE, OAE, are excluded also by the fifth general rule, 
because they have universal conclusions with a particular 
premiss. 

Four, viz., AAE, AAO, AIO, IAO, because they have 
negative conclusions without any negative premiss. 

To which must be added IEO, for an illicit process of the 
major in every figure. a 

Fifty-three moods (16 + 12+12 + 8 + 4 + 1) are 
therefore excluded, many of which offend against several 
rules, although one alone is noted. 

The following is a list of the eleven legitimate moods, viz., 
AAA, AAI, AEE, All, AEO, AOO, EAE, EAO, EIO, 
IAI, OAO. 

But these moods cannot be used legitimately in each figure, 
for the first excludes all such as have not a universal major 
and an affirmative minor. Six of the above moods, therefore, 
can only be used legitimately in the first figure, viz., AAA, 
AAI, All, EAE, EAO, EIO. 

But of these two AAI and EAO, although conclusive, are 
useless in the first figure, since, instead of a particular, the 
premisses warrant a universal conclusion ; for the minor 
term, being universal in the minor proposition, may be uni- 
versal also in the conclusion. There are therefore only four 

a IEO has been condemned ever since the days of Apuleius, as far as the 
second and third figures are concerned. It was sometimes allowed in the first, 
as the indirect mood Frisesmo, but should not have been retained by Aldrich, 
who does not recognise the indirect moods. With a direct conclusion, it mani- 
festly produces an illicit process of the major term. — Mansell, p. 65. 



MANUAL OF LOGIC. 159 

moods used in the first figure, viz., AAA, EAE, All, EIO. 

The following are examples : — 

bAr — Every effect is the result of an adequate cause. 

b A — The world is an effect ; therefore, 

rA. — The world is the result of an adequate cause. 

cE— No subject of a highly solemn character is suited to 

poetry. 
lA — Religion is a subject of a highly solemn character ; 

therefore, 
rEnt. — Religion is not suited to poetry. 

dA — All comets are irregular planets. 
rI — Some luminous bodies are comets. 
I. — Some luminous bodies are irregular planets. 

fE — No afflictions of nature are disgraceful. 

rT — Some personal deformities are afflictions of nature. 

O. — Some personal deformities are not disgraceful. 

In the second figure no mood can be used legitimately in 
which the major is not universal and the conclusion negative. 
The legitimate moods of the second figure are consequently 
five, viz., AEE, AOO, EAE, EAO, EIO. But of these 
EAO would be useless, as the premisses warrant a universal 
conclusion. Hence the moods used in the second figure are 
only four, viz., EAE, AEE, EIO, AOO, e. g 

cEs — No ruminant animals are predaceous. 

A — The lion is predaceous. 

rE. — The lion is not a ruminant animal. 

cAm — Every planet describes an orbit. 
Es — The sun does not describe an orbit. 
trEs. — The sun is not a planet. 

fEs — No man of strict veracity sports with truth. 

tI — Some jocose men sport with truth. 

nO. — Some jocose men are not of strict veracity. 



1 60 MANUAL OF LOGIC. 

bA — All honest reasoners weigh the arguments of an 

opponent with caution. 
rOk — Some sectaries do not weigh the arguments of an 

opponent with caution ; therefore, 
O. — Some sectaries are not honest reasoners. 

In the third figure no moods can be used except those whose 
minor is affirmative, and whose conclusion is particular. Of 
these there are six, viz., AAI, All, EAO, EIO, I AT, OAO. 
None of these is useless, because although the minor be A, 
yet the minor term is particular in it as its predicate, and 
must therefore be particular in the conclusion. The follow- 
ing are examples of all the moods : — 

dA — All who assist in the progress of true science deserve 

the respect of mankind. 
rAp — All who assist in the progress of true science have 

to contend with difficulties. 
tI. — Some who have to contend with difficulties deserve 

the respect of mankind. 

dIs — Some acts of friendship are acts which militate against 

justice. 
Am — All acts of friendship appear virtuous and splendid to 

the thoughtless. 
Is. — Some things which appear virtuous and splendid to 

the thoughtless militate against justice. 

dA — All moral agents are responsible for their conduct. 
tIs — Some moral agents are subject to severe temptations. 
I. — Some subject to severe temptations are responsible for 
their conduct. 

fE — No branch of science is altogether perfect. 
lAp — All branches of science are worthy of diligent culture. 
tOn. — Some things worthy of diligent culture are not alto- 
gether perfect. 



MANUAL OF LOGIC. 161 

bOk — Some distinguished poets have not escaped poverty. 
Ar — All distinguished poets do honour to their country. 
dO. — Some who do honour to their country have not 
escaped poverty. 

fE — No bombastic writers are worthy of imitation. 

rIs — Some bombastic writers are amusing. 

On. — Some things amusing are not worthy of imitation. 

In the fourth figure the legitimate moods are five, viz., 
AAI, AEE, EAO, EIO, and IAI. The following are ex- 
amples of all the moods :— 

br Am — All wise statesmen legislate with caution. 

An — All who legislate with caution regard the interests of 

the community. 
tIp. — Some who regard the interests of the community 

are wise statesmen. 

cAm — All the planets are opaque bodies. 

En — No opaque bodies are capable of transmitting light in 

any other way than by reflection. 
Es. — No bodies capable of transmitting light in any other 

way than by reflection are planets. 

dIm — Some learned men are deeply involved in prejudice. 
Ar — All who are deeply involved in prejudice are sus- 
picious advisers. 
Is. — Some suspicious advisers are learned men. 

fEs — No factious man is truly religious. 
Ap — All truly religious men are charitable. 
O. — Some charitable men are not factious. 

frEs — No fallacious argument is a legitimate mode of per- 
suasion. 

Is — Some legitimate modes of persuasion fail in convincing. 

On. — Some things which fail in convincing are not falla- 
cious arguments. 



162 MANUAL OF LOGIC 

Although eleven moods were stated to be admissible, yet 
some of them occur in more than one figure ; and since each 
separate occurrence is reckoned a new mood, from this re- 
currence of the same symbols in different figures, there are 
reckoned in all nineteen moods. 

On examining the vowel symbols used to represent the 
moods admissible in the different figures, it will be found 
that of the eleven legitimate moods six occur twice in different 
figures, viz., AAI in Darapti and Bramantip, AEE in Ca- 
mestres and Camenes, All in Darii and Datisi, IAI in Disa- 
rms and Dimaris, EAE in Cesare and Celarent, and EAO in 
Felapton and Fesapo. The mood EIO occurs in all the 
figures, viz., in Ferio, Festino, Ferison, and Fresison. Add 
to these, three moods that only occur once, viz., AEO, AOO, 
OAO, and we have nineteen moods. 

For these nineteen moods logicians have formed certain 
names, which serve to denote the mood and figure ; for it has 
been shown that the same mood is used in different figures. 
Hence the vowels which denote the mood would not alone 
point out the figure, and they have therefore been incorpo- 
rated in words which are of great use in reduction, as will be 
hereafter seen. 

The names are exhibited in the following lines, which 
mention also the figures to which they respectively belong : — 

Barbara, Celarent, Darii, Ferioque prioris. 

Cesare, Camestres, Festino, Baroko secundae. 

Tertia, Darapti, Disarms, Datisi, Felapton. 

Bokardo, Ferison habet, Quarta insuper addit. 

Bramantip, Camenes, Dimaris, Fesapo, Fresison. 

In addition to these, there are five nameless moods, viz., 
AAI and EAO in the first figure, AEO and EAO in the 
second figure, and AEO in the fourth. These are deemed 
superfluous, being superseded by other moods, having the 
same premisses with universal conclusions ; for the conclu- 
sions in the nameless moods are all particular, and may be 



MANUAL OF LOGIC. 163 

considered as deduced by subalternation from the universal 
conclusions. And since the truth of the universal implies the 
truth of the particular, the nameless moods are of no practical 
use in strict argument, for it is needless to infer a particular 
where a universal conclusion can be deduced. 

These moods, although useless, are not illegitimate. 

There are no useless moods in the third figure, for a uni- 
versal conclusion cannot be drawn in that figure. 

The mood AAA belongs exclusively to the first figure. It 
is excluded from the second, because the mood is affirmative ; 
from the third, because the conclusion is universal, and from 
the fourth, because in that figure the conclusion is always 
particular when the minor is affirmative. 

A universal affirmative conclusion can be deduced only 
from two universal affirmative premisses in the first figure, in 
the mood Barbara. 

Universal negative conclusions may be proved by the first 
figure in Celarent, by the second figure in Cesar e and 
Camestres, and by the fourth figure in Camenes. 

Particular affirmative conclusions may be proved in the 
first figure by Darii, and the nameless mood, AAI, by the 
third figure in Darapti, Disamis, and Datisi, by the fourth 
figure in Bramantip and Dimaris. 

Particular negative conclusions may be proved by each of 
the figures, viz., in Ferio of the first, Festino and Baroko 
of the second, Felapton, Bokardo, and Ferison of the third, 
Fesapo and Fresison of the fourth, together with the subal- 
ternates of the four moods by which universal negatives are 
proved. 



164 MANUAL OF LOGIC. 

SECTION II. 
REDUCTION OF SYLLOGISMS. 

The first figure of syllogism is considered perfect? and the 
other three as imperfect, although the same designations are 
given to moods under each. 

The first figure is said to be perfect, for two reasons — 

1. It proceeds directly and immediately on the Dictum de 
omni et de nullo ; and, 2. It arranges the terms in the most 
natural order, so as to show at once their mutual relations. 

The first figure asserts in the major proposition, that an 
attribute expressed by the predicate is found in a whole class 
without exception, that class being expressed by the subject of 
the proposition, and states in the minor proposition, that an- 
other class or part of it, expressed by the subject, is contained 
within the former class, now the predicate of the minor, and 
it is therefore inferred that the subordinate class has all the 
qualities found in the larger class to which it belongs. This 
may be seen more clearly from an analysis of the following 
syllogism : — 

Every effect has a cause. 
Gravitation is an effect. 
Gravitation has a cause. 

This syllogism exemplifies the Dictum de omni. The pre- 
dicate 'cause,' in the major proposition, is affirmed of every- 

a In some logical treatises, perfect and imperfect syllogisms are confounded 
with the direct and indirect. The latter designations are an innovation of the 
schoolmen. In an indirect syllogism, properly speaking, the minor is the^re- 
dicate, and the major the subject of the conclusion, and from which the immediate 
conclusion is not inferred, but its converse. In a direct mood the predicate of 
the conclusion is the major term. 



MANUAL OP LOGIC. 165 

thing that can be termed an ' effect,' without any exception. 
Now the singular term ' gravitation,' the subject of the 
minor proposition, is contained in the common term 'effect,' 
which latter term is now the predicate of the minor. Hence 
if the predicate can be affirmed of everything represented by 
the common term ' effect,' it may also be affirmed of any one 
thing contained under it. 

The following syllogism, viz. — 

No man is infallible, 
The Pope is a man, 
The Pope is not infallible, 

exemplifies the Dictum de nullo. The predicate ' infallible,' 
in the major proposition, is denied of every individual con- 
tained under the common term ' man ' without any excep- 
tion. But the singular term 'Pope,' the subject of the 
minor proposition, is contained in the common term ' man,' 
which latter term is now the predicate of the minor. Hence 
since the predicate ' infallible ' is denied of everything de- 
noted by the common term ' man,' it may also be denied of 
any individual contained under it. 

In the other figures the ' Dictum ' is applied indirectly and 
partially, and the relation of the terms is not shown by their 
position. The first figure, therefore, institutes the most ob- 
vious comparison of the extremes, and furnishes conclusions of 
all kinds, while the other figures furnish only certain kinds 
of conclusions. 

It must be remembered, however, that the principle of the 
first figure is implied in all the other figures, notwithstanding 
their peculiarities, and that it is the presence of this principle 
that warrants their reduction. 

To reduce a syllogism is to bring an imperfect mood to a 
perfect, i. e., to reduce a syllogism drawn in any of the last 
three figures to a corresponding figure of the first, by altering 
the arrangement of the premisses. By this process the 



166 MANQAL OF LOGIC. 

arrangement of the terms is not only improved, but the com- 
parison is rendered closer, and the conclusion more obvious, 
as we then can apply to each, as the case may be, the Dictum 
de omni et de nullo. Hence reduction is often called demon- 
stration, because it shows the validity of imperfect moods 
by bringing them to corresponding moods of the first figure, 
which furnish either the same conclusions or such as are equi- 
valent by conversion. 

The imperfect mood to be reduced is called the reducend, 
and that to which it is reduced the reduct. 

Reduction is of two kinds — 

1 . Direct or ostensive reduction. 

2. Indirect or reductio per impossible. 

Ostensive reduction consists in bringing the premisses of 
the reducend to a corresponding mood in the first figure, by 
transposition or conversion of the premisses, and from the 
premisses thus changed, deducing either the original conclu- 
sion or one from which it follows by conversion. 

In this species of conversion no new terms or propositions 
are introduced ; those of the reducend being either transposed 
or converted. The validity of ostensive reduction depends on 
the perfection of the reduct ; for since the reduct, being a 
perfect mood of the first figure, must yield a true conclusion, 
it is inferred that the original conclusion of the reducend is 
true, because it is found to be the same with the conclusion of 
the reduct, or implied in it. 

Indirect reduction, or reductio per impossible, properly so 
called, consists in the following process : — From one of the 
premisses of the reducend, and the contradictory of its con- 
clusion, new premisses are formed agreeably to a correspond- 
ing mood in the first figure ; and from these a conclusion is 
drawn, contradicting the other premiss which is omitted. The 
reduction is called indirect, because it does not positively 
prove the original conclusion to be true, but merely shows 
that an absurdity follows the supposition of its being false. 



MANUAL OF LOGIC. 167 

The validity of this process depends on the principle of 
contradictory opposition, viz., that of contradictory proposi- 
tions, one is always false, and the other true. If, therefore, 
the original premisses of the reducend be true, as is always 
supposed, then a conclusion, which contradicts any of them, 
must be false ; but as that false conclusion is deduced from 
the new premisses, one of them must also be false, and that 
must be the contradictory of the original conclusion. 

This is the common process by which some imperfect 
moods are reduced ; but it will be found that these moods 
admit of direct reduction, by means of conversion by negation 
or contraposition. Thus, reduction may be confined to one 
kind, direct or ostensive. 

In any case, however, all conclusions may be proved by 
one or other of the two modes, viz., the direct or indirect. 
The direct mode shows the original conclusion to be true, by 
arranging the data from which it is deduced in such a way 
as to show that it results from them necessarily, -so that the 
mind cannot deny the truth of the conclusion, after admitting 
the truth of the premisses. In the indirect mode, on the 
other hand, the conclusion is assumed to be false ; and thus 
assumption results in some palpable absurdity, showing, as a 
necessary consequence, that this assumption must have been 
false ; and hence the conclusion, which was pro forma, 
assumed to be false, must in reality have been true. This 
latter mode is probably the more forcible and convincing. 

In direct reduction, the imperfect moods are reduced to the 
perfect, by various processes of transposition, conversion, or 
contraposition. These processes are indicated by the principal 
consonants, in the technical words which designate the 
moods. 

1. The initial consonant indicates that the mood expressed 
by the word is reducible to a mood of the first figure, the 
name of which commences with the same letter, e. g., all 
moods designated by words commencing with B, viz., Baroko, 



168 MANUAL OF LOGIC. 

Bokardo, Bramantip, are reducible to Barbara ; those with 
C, viz., Cesare, Camestres, Camenes, are reducible to Cela- 
rent ; those with D, viz., Darapti, Datisi, Disamis, Dima- 
ris, are reducible to Darii ; and those with F, viz., Festino, 
Felapton, Ferison, Fesapo, Fresison, are reducible to Ferio. 

2. The letter M indicates, that in the mood expressed by 
the name in which it occurs, the premisses must be trans- 
posed, so that the major of the reducend becomes the minor 
in the reduct, and vice versa, e. g., in reducing Camestres, of 
the second figure, to Celarent of the first, M shows that the 
premisses must be transposed, to give them the requisite 
arrangement. The same process is followed in reducing 
Bramantip to Barbara, Camenes to Celarent, Disamis and 
Dimaris to Darii. 

3. The letters S and P show generally that in reducing the 
moods expressed by the names in which they occur, the pro- 
position designated by the vowel preceding each must be con- 
verted in the reduct. S denotes simple conversion, and P 
accidental conversion (conversio per accidens), e. g., in re- 
ducing Cesare, of the second figure, to Celarent, of the first. 
S shows that the major proposition E is to be converted 
simply, so as to bring the predicate or middle term to the 
place of the subject, as in the first figure. Again, in reducing 
Felapton, of the third figure, to Ferio of the first, the minor 
proposition A must be converted per accidens, so as at once 
to become a particular affirmative, and bring the subject, the 
middle term, to the place of the predicate, as in the first 
figure. 

4. The letter K indicates that the moods undergo indirect 
reduction by contradiction or contraposition : by contradiction 
when the contradictory of the conclusion is substituted for the 
premiss designated by the vowel after which K is placed ; — 
by contraposition (or conversion by negation) when the 
quality of the propositions is changed, so as to bring them to 
a state in which they may be directly reduced. 



MANUAL OF LOGIC. 169 

It must be remembered that these letters are intended to 
apply to the vowels which precede, and not to those which 
follow them. 

In reducing syllogisms directly, the process is much more 
simple in some cases than in others, e. g., Cesare and Festino, 
of the second figure, may be reduced to Celarent and Ferio? 
by simply converting the major premiss, as may be seen from 
the annexed examples : — 

1. Cesare. 

No man of honour is addicted to equivocation. 
All liars are addicted to equivocation. 
No liars are men of honour. 

Reduced to Celarent — 

No man addicted to equivocation is a man of honour. 
All liars are addicted to equivocation. 
No liars are men of honour. 

2. Festino. 

No man of strict veracity sports with truth. 

Some jocose men sport with truth. 

Some jocose men are not men of strict veracity. 

Reduced to Ferio — 

No man sports with truth who is of strict veracity. 

Some jocose men sport with truth. 

Some jocose men are not of strict veracity. 

In like manner, Datisi and Ferison, of the third figure, 
may be reduced to Ddrii and Ferio, by the simple conversion 
of the minor. Thus — 

1. Datisi. 
All moral agents are responsible for their conduct. 

H 



1 70 MANUAL OF LOGIC. 

Some moral agents are subject to severe temptations. 
Some subject to severe temptations are responsible for their 
conduct. 

Reduced to Darii — 

All moral agents are responsible for their conduct. 
Some subject to severe temptations are moral agents. 
Some subject to severe temptations are responsible for their 
conduct. 

2. Ferison. 

No men addicted to prejudice possess powerful minds. 
Some men addicted to prejudice are learned. 
Some learned men do not possess powerful minds. 

Reduced to Ferio — 

No men addicted to prejudice possess powerful minds. 
Some learned men are addicted to prejudice. 
Some learned men do not possess powerful minds. 

In reducing Darapti and Felapton, of the third figure, to 
Darii and Ferio, it is merely necessary to convert the minor 
per accidens. Thus — 

1. Darapti. 

All who assist in the progress of true science deserve the 
respect of mankind. 

All who assist in the progress of true science have to con- 
tend with difficulties. 

Some who have to contend with difficulties deserve the 
respect of mankind. 

Reduced to Darii — 

All who assist in the progress of true science deserve the 
respect of mankind. 



MANUAL OF LOGIC. 171 

Some have to contend with difficulties who assist in the 
progress of true science. 

Some have to contend with difficulties who deserve the 
respect of mankind. 

2. Felapton. 

No branch of science is altogether perfect. 
All branches of science are worthy of diligent culture. 
Some things worthy of diligent culture are not altogether 
perfect. 

Reduced to Ferio — 

No branch of science is altogether perfect. 

Some things worthy of diligent culture are branches of 
science. 

Some things worthy of diligent culture are not altogether 
perfect. 

In reducing Fresison, of the fourth figure, to Ferio, both 
the major and minor are converted simply — 

1. Fresison. 

No fallacious arguments are legitimate means of persuasion. 
Some legitimate means of persuasion fail in convincing. 
Some things which fail in convincing are not fallacious 
arguments. 

Reduced to Ferio — 

No legitimate means of persuasion are fallacious arguments. 

Some things which fail in convincing are legitimate means 
of persuasion. 

Some things which fail in convincing are not fallacious 
arguments. 

In reducing Fesapo, of the fourth figure, to Ferio, the 



1 72 MANUAL OF LOGIC. 

major is converted simply, and the minor per accidens. Thus — 

1. Fe&apo. 
No factious man is truly religious. 
All truly religious men are charitable. 
Some charitable men are not factious. 

Reduced to Ferio — 
No truly religious man is factious. 
Some charitable men are truly religious. 
Some charitable men are not factious. 

In reducing Dimaris and Camenes, of the fourth figure, to 
Darii and Celarent, the premisses are transposed, and the 
conclusion converted simply. Thus — 

1. Dimaris. 
Some learned men are egotistical. 

All egotistical men are fond of popularity. 
Some fond of popularity are learned men. 

Reduced to Darii — 

All egotistical men are fond of popularity. 

Some learned men are egotistical. 

Some learned men are fond of popularity. 

2. Camenes, 

All useful studies are worthy of encouragement. 

Nothing worthy of encouragement is injurious to the morals. 

Nothing injurious to the morals is a useful study. 

Reduced to Celarent — 

Nothing worthy of encouragement is injurious to the morals. 

All useful studies are worthy of encouragement. 

No useful study is injurious to the morals. 

In reducing Ca?nestres, of the second figure, to Celarent, 
the premisses are transposed, and the minor and conclusion 
converted simply. Thus — 



MANUAL OV LOGIC. ] 73 

Camestres. 
Every man of sense is anxious to gain useful information. 
No idle man is anxious to gain useful information. 
No idle man is a man of sense. 

Reduced to Celarent — 

No person who is anxious to gain useful information is an 
idle man. 

Every man of sense is anxious to gain useful information. 
No man of sense is an idle man. 

In reducing Disamis, of the third figure, to Darii, the pre- 
misses are transposed, and the major and conclusion converted 
simply. Thus — 

Disamis. 

Some poets prefer sound to sense. 

All poets dislike to be severely criticised. 

Some who dislike to be severely criticised prefer sound to sense . 

Reduced to Darii — 
All poets dislike to be severely criticised. 
Some who prefer sound to sense are poets. 
Some who prefer sound to sense dislike to be severely 
criticised. 

In reducing Bramantip, of the fourth figure, to Barbara, 
the premisses are transposed, and the conclusion converted per 
accidens. Thus — 

Bramantip. a 

All blasphemous writers injure the public morals. 

a The reason why in this mood the conclusion may be accidentally converted 
is, that the major term has been distributed in the major premiss, and therefore 
is distributable in the conclusion, although, owing to the figure, it cannot be dis- 
tributed, for a term should not be distributed in the conclusion, if it has not 
been distributed in its premiss ; and it should be remembered also, that a term 
ought not to be undistributed in the conclusion, if it has been undistributed in 
its premiss. 



174 



MANUAL OF LOGIC. 



All who injure the public morals deserve punishment. 
Some who deserve punishment are blasphemous writers. 

Reduced to Barbara — 

All who injure the public morals deserve punishment. 
All blasphemous writers injure the public morals. 
All blasphemous writers deserve punishment. 

The following table presents summarily the various pro- 
cesses by which imperfect Moods are reduced to perfect : — 



REDUCEKDS. 


REDTJCTS. 


PROCESSES. 


Cesare 


Celarent 


Major premiss converted simply. 


Camestres 


Celarent 


Premisses transposed. Minor and con- 
clusion converted simply. 


Festino 


Ferio 


Major converted simply. 


Darapti 


Darii 


Minor converted per accidens. 


Disamis 




Premisses transposed. Major and con- 
clusion converted simply. 




Datisi 


Darii 


Minor converted simply. 


Felapton 


Ferio 


Minor converted per accidens. 


Ferison 


Ferio 


Minor converted simply. 


Bramantip 


Barbara 


Premisses transposed. Conclusion con- 
verted per accidens. 


Camenes 




Premisses transposed. Conclusion con- 
verted simply. 






Darii 


Premisses transposed. Conclusion con- 
verted simply. 






Ferio 


Major converted simply. Minor per 
accidens. 








Ferio 


Major and Minor converted simply. 





MANUAL OF LOGIC. 



175 



Examples of all the Moods in the three last figures (except 
Baroko and Bokardo) converted to the corresponding figures 
of the first : — 



SECOND FIGURE. 



FIRST FIGURE. 



u /No planet is fixed convert simply \ g /No fixed body is a planet. 

| -j Every star is fixed as it is F *H Everv star is fixed. 

P v No star is a planet as it is ' £> * No star is a planet. 



3 ( r transpose the 

£ Every star is fixed 3 premisses, and 

| \ No planet is fixed f simply convert 

C the minor 
No planet is a star convert simply 



§{ 



No fixed body is a planet. 
Every star is fixed. 
No star is a planet. 



{No planet is a sun convert simply 
Some luminous bodies are") a$ a ^ 
suns i 
Some luminous bodies are") as it is 
not planets $ 



/■No sun is a planet. 
.o j Some luminous bodies are 
S -j suns. 
•*< I Some luminous bodies are 

V not planets. 



THIRD FIGURE. 



FIRST FIGURE. 



.„ /All flowers are beautiful.... as it is 
| J All flowers are deciduous... { C ° c ™Zly 
| I Some deciduous things are) ag u & 
^ \ beautiful ) 



r All flowers are beautiful. 
Some deciduous things are 

flowers. 
Some deciduous things are 

beautiful. 



« (Some flowers are deciduous ^Sv convert ) 
| I All flowers are beautiful.... £ ^mljor ' 

^ l s ridS^!.. t ^ g !.r}--^^ 



All flowers are beautiful. 
Some deciduous things are 

flowers. 
Some deciduous things are 

beautiful. 



'.Sj C All flowers are beautiful as it is 

■*| < Some flowers are 
q (.Some plants are 



sautiful as it is ~% -s r All flowers are 

plants convert simply > e < Some plants ar 

beautiful., as it is 3 Q C Some plants ar 



beautiful, 
are flowers, 
plants are beautiful. 



No star is dark as it is 

All stars are distant { C °Za'rly ^ 

Some things distant are not! „„ -, • 
dark $<uttts 



{No star is dark. 
Some things distant &ve 
stars. 
Some things distant are not 
dark. 



a ( No star is dark as it is 

.§ J Some stars are unseen convert simply 

h 1 Some things unseen are not") .. . 
% { dark...... \asttts 



}l 



(No star is dark. 
Some unseen things are stars 
Some unseen things are not 
dark. 



FOURTH FIGURE. 



FIRST FIGURE. 



' E g e em , P y e ?^ U .?..?. t .° n . e ... iS ... a Vranspose the 
Every gem is brilliant'.".'.!!! J P remisses 
Some brilliant stones are! change to uni- 

' precious $ versal 



Every gem is brilliant. 

Every precious stone is a 
gem. 

All precious stones are bril- 
liant. 



3 76 MANUAL OF LOGIC. 

2 r Every star is a fixed body...-i transpose tke~\ "g rNo fixed body is a planet- 

| < No fixed body is a planet.... -> premisses > § < Every star is a fixed body. 

<o LNo planet is a star convert simply J k$ CNo star is a planet. 

/Some luminous bodies are"} , /All comets are irregular 

g comets Ctransvose I :«• planets. 

5 I All comets are irregular \ p £ J Some luminous bodies are 

' planets J (§1 comets. 

Some irregular planets are! „_.,^ w «: mn r,. I I Some luminous bodies are 

luminous bodies J convert sim P® J \ irregular planets. 

"No falling body is a star.. . . convert simply \ ( No star is a falling body. 

^ I All stars are luminous convert panic, f "g J Some I'nous bodies are stars 

g ) Some luminous bodies are") v • I (2 I Some luminous bodies are 

^ C not falUng bodies J as " ls J ^ { not falling bodies. 

§ rNo fixed body is a comet. . . convert simply ") ( ^T^JLt^^^ 

.§ NSome comets are luminous convert simply / | J So ™ * 1 <l mmouS b ° dieS are 

8 J Some luminous bodies are! . . f £ 1 <, come , ls - . . „ 

I" f nntfiir "wi"e» "''■v I as a is \ **< Some luminous bodies are 

^ notnxea -> -» ( not fixed bodies. 






SECTION III. 

Reductio per impossible, or ad Absurdum. 

This species of reduction, as already partially explained, 
consists in the hypothetical falsehood of that which is under 
discussion; and in the tracing of such a concession to its 
legitimate consequences, with the view of proving that what 
was hypothetically conceded as false, involves some palpable 
impossibility or absurdity. 

This kind of reduction is usually confined to the moods 
Baroko of the second, and Bokardo of the third figure. 
It is equally applicable, however, to any of the three last 
figures, as will be shown by examples. But let us, in the 
first place, take Baroko and Bokardo. 

In reference to Baroko and Bokardo, it is necessary to re- 
mark that the contradictory of the conclusion must be substi- 
tuted for the particular negative premiss, while the universal 
premiss retains its original place. In other moods reducible 
in this way, the contradictory of the conclusion must be sub- 
stituted for the major or minor premiss, as the requirements 
of a syllogism in the first figure may render such substitu- 
tion necessary. 



MANUAL OF LOGIC. 177 

1. Baroko. 
bA — All truly wise men live virtuously. 
rOk — Some philosophers do not live virtuously ; therefore, 
O. — Some philosophers are not truly wise men. 

If instead of the minor (a particular negative) we substi- 
tute the contradictory of the conclusion, viz., 

All philosophers are truly wise men, 

the middle term will be universally affirmed of the major in 
the major proposition, while in the new minor proposition it 
will be affirmed that the whole minor term is contained in the 
major, and by the Dictum de omni the conclusion will follow 
that the middle term is affirmed of the whole minor. By thus 
substituting the contradictory of the conclusion, in place of 
the minor (a particular negative), the syllogism will stand 
thus — 

Barbara. 

bAr — All truly wise men live virtuously. 

bA — All philosophers are truly wise men ; therefore, 

rA. — All philosophers live virtuously. 

The conclusion of the reduct is the contradictory of the 
original minor premiss of the reducend, and must be false, 
since the premisses of the reducend were supposed to be true ; 
and therefore one of the premisses of the reduct, from which 
the conclusion has been legitimately deduced, must also be 
false. But as the major proposition is one of the original 
premisses granted to be true, the falsity must be in the minor, 
viz., the contradictory of the original conclusion, which 
proves the original conclusion to be true. 

2. Bokardo. 
bO — Some kinds of money have not intrinsic value. 
kAr — All kinds of money have adventitious value. 
dO Some things having adventitious value have not in- 
trinsic value. 

h2 



178 MANUAL OF LOGIC. 

If in place of the negative premiss (the major), we substi- 
tute the contradictory of the conclusion, viz. — 

All things having adventitious value have intrinsic value. 

We shall have the following syllogism in Barbara, viz. — 

All things having adventitious value have intrinsic value. 
All kinds of money have adventitious value. 
All kinds of money have intrinsic value. 

This new conclusion must be false, because it contradicts 
the major premiss of the reducend; therefore the substituted 
major premiss, from which the conclusion of the reduct is 
drawn, must be false, and consequently its contradictory (the 
conclusion of the reducend) must be true. 

But although the moods Baroko and Bokardo are usually 
reduced, by reductio per impossible, to Barbara, they may 
also be ostensively reduced by contraposition or negation — 
the first to Ferio, and the second to DariL Let the follow- 
ing syllogism be in Baroko : — 

Every true patriot is a friend to religion. 

Some great statesmen are not friends to religion. 

Some great statesmen are not true patriots. 

In order to reduce this syllogism to Ferio, we first convert 
the major premiss by negation, and then render the minor 
premiss affirmative, by combining the negative particle with 
the predicate. Thus — 

He-who-is-not-a-friend-to-religion is not a true patriot. 
Some great statesmen are not-friends-to-religion. 
Some great statesmen are not true patriots. 

In like manner, Bokardo may be reduced to Darii. Let 
the following syllogism be in Bokardo : — 

Some systems of unjust exaction have not been followed by 
immediate punishment. 



MANUAL OF LOGIC. 179 

All systems of unjust exaction incur guilt. 
Some things which incur guilt have not been followed by 
immediate punishment. 

In reducing this example to Darii, we first transpose the 

premisses, and next convert the major by contraposition. 

Thus- 
All systems of unjust exaction incur guilt. 
Some things which have not been followed by immediate 

punishment are systems of unjust exaction ; therefore, 

Some things which have not been followed by immediate 

punishment incur guilt. 

It has been stated above, that the moods in the three last 
figures may be reduced to the first by the reductio per im- 
possible, as well as Baroko and Bokardo. To assist the 
learner in the way in which this may be done, the following 
example is annexed : — 

Let the mood to be reduced be in Disamis, of the third 
figure. 

This mood is represented by the vowel symbols, IAI. If 
this conclusion I is false, its contradictory E, must be true ; 
for of contradictories one must be false, and the other true. 
Now, this assumed contradictory E contradicts the major 
premiss I. If we substitute this contradictory for I, the new 
premisses will be EA, from which we can legitimately deduce 
the conclusion E, and the new mood will be Celarent of the 
first figure. The falsity involved in this assumed contradic- 
tory will be best illustrated by examples of the reducend and 
reduct : — 

dI — Some infidels publish their opinions. 
sA — All infidels are opposed to true religion. 
mIs. — Some beings opposed to true religion publish their 
opinions. 



180 MANUAL OF LOGIC. 

This syllogism, when reduced per impossible, is as follows : — 

cE — No beings opposed to true religion publish their opinions. 
lA — All infidels are opposed to true religion. 
kEnt. — No infidels publish their opinions. 

In this reduction the conclusion of the reducend was 
assumed to be false, and its contradictory assumed to be true, 
and from the contradictory assumed to be true, united to 
the minor premiss of the reducend, a new conclusion 
was drawn ; but this conclusion is obviously false, because it 
contradicts the major premiss of the reducend, which was 
assumed to be true. Hence it must follow, that the contra- 
dictory of the reducend (which was assumed true) is in 
reality false ; and hence the conclusion of the reducend must 
itself be true. 

It has been observed, that in reducing the moods Baroko 
and Bokardo per impossible, the assumed or new conclusion 
directly contradicts an original premiss of the reducend. In 
the other moods, however, which may be reduced in this 
way, the assumed or new conclusion will not in every 
instance directly contradict an original premiss of the redu- 
cend. The contradicted premiss may be one deducible from 
the original proposition, or its simple or accidental converse ; 
for by the laws of conversion, if a proposition is true, the 
particular contained under it is true, and so also is its simple 
or accidental converse ; and the contradiction of any of these 
will prove that the original conclusion cannot be false, equally 
as well as if the original premiss were itself contradicted. 

OF COMPOUND PROPOSITIONS. 

Compound propositions* have been variously classified, but, 

a The curious in compound propositions are referred to Dr Kirwan's Logic, 
vol. I., where they will find the subject as amply and satisfactorily treated as 
anywhere. 



MANUAL OF LO^IC. 181 

generally speaking, with questionable success. This has 
chiefly arisen from an uudue multiplication of names, founded 
on distinctions comparatively non-essential. Many of them 
are now very properly disappearing from logical treatises, and 
all intended here is a mere enumeration. 

1. Cojmlative Propositions. 

A copulative 11 proposition is one which has its subjects or 
predicates joined by copulative or negative particles. 

A proposition of this kind may have several subjects, and 
but one predicate ; as, 

Caesar and Pompey were great generals. 
Neither gold nor silver will purchase immortality. 

Or several predicates, and but one subject ; as, 

Caesar was a great and a fortunate general. 
Or several subjects and several predicates ; as, 

Cato, Varro, Cicero, and Seneca cultivated logic, physics, 
metaphysics, and ethics. 

When the connecting particle is and, the proposition is a 
copulative affirmative ; but when the particle is not, neither, 
&c, the proposition is a copulative negative. 

A copulative affirmative is false, if any of the parts is false ; 
for the truth of such a proposition depends on the truth of all 
its parts. The proposition, 

The earth and moon revolve round the sun, 

would be false if the predicate, i revolve round the sun,' did 
not apply to both. On the other hand, a copulative negative 
is false, if either of the parts is true ; as, 

Virtue and riches are not necessary to salvation. 

a The number of simple propositions into which a copulative may be re- 
solved is determined by multiplying the number of subjects into that of the pre- 
dicates. — Thynne. 



182 MANUAL OF LOGIC. 

2. Disjunctive Propositions. 

A disjunctive proposition is one in which the whole sub- 
ject is said to be contained in two or more predicates, con- 
nected by a disjunctive particle, e. g. — 

All wars are either just or unjust. 

Every animal is either rational or irrational. 

The parts of a disjunctive proposition are always affirmative 
in quality, and the proposition is true, if any of its parts is 
true, e. g. — 

The true religion is either the Mahometan, or Jewish, or 
Christian. 

But if it can be shown that none of the parts is true, the pro- 
position is false ; as, 

The true religion is either the Mahometan or Jewish. 

The truth of a disjunctive proposition depends on the 
necessary opposition of the parts ; for since a division is made 
in every disjunctive proposition, it must be subject to the 
rules of logical division. The predicates are the parts into 
which the whole subject is divided; and it is therefore neces- 
sary that the predicates taken together should contain no 
more and no less than the whole subject. Thus — 

The teeth are either incisors, canine, bicuspid, or molar. 

3. Conditional Propositions. 

A conditional* proposition is one in which the assertion is 
made under a condition. 

a In the scheme of division and subdivisions of propositions laid down (p. 104), 
the usual method was followed of dividing hypothetical propositions into condi- 
tional and disjunctive ; the matter not appearing of such importance as to ren- 
der any alteration in the ordinary scheme necessary. But as it is not intended 
to treat either of hypothetical propositions or syllogisms separately, but to 
employ both as synonymous with the conditional, it may be necessary to 
state that a division of hypothetical propositions into conditional and disjunctive, 
is illogical, for hypothetical and conditional propositions are identical in sense, 



MANUAL OF LOGIC. 183 

The part, or branch of the proposition in which the condi- 
tion occurs, is called the antecedent, and the part or branch 
which follows from it the consequent. The connection be- 
tween them is called the consequence. 

The antecedent and consequent cannot always be distin- 
guished by their order. The antecedent is that which must 
have the conditional particle prefixed, and may be distin- 
guished in this way, although it should follow the consequent 
in the verbal arrangement of a sentence. 

In a conditional proposition, there is no absolute assertion 
made as to the truth of either the antecedent or consequent. 
The conditions are, that if the antecedent is true, the conse- 
quent must be true ; in other words, that if the antecedent is 
granted, the consequent may be inferred. Hence if there be 
a vis consequently in the inference, the proposition will be 
true, though one or both of the parts be false, e. g. — 

If there be no providence, there will be no future state. 
In this proposition both antecedent and consequent are false; 
yet the proposition, as a whole, is true, for the consequent 
follows from the antecedent. But, on the other hand, both 
of the parts may be true, and the proposition itself false, if 
there be no vis consequentice, e. g. — 

If Cicero was a Roman, he was a patriot. 

and differ only to the extent of being names appropriated from different lan- 
guages ; so that in the division referred to, the name of a genus is confounded 
with that of a species. It may be mentioned, also, that this division has not 
even tbe sanction of authority; for Boethius, the chief authority on this point, 
employs indifferently the terms hypotheticus, conditionalis, non simplex, for the 
genus, and as opposed to categoricus or simplex. — [See Ed. Rev., vol. lvii., 
p. 219.] Mr Mansel is of opinion, tbat ' with reference to modern usage, it 
will be better to contract the Greek word than to extend the Latin one ;' and 
therefore uses the term hypothetical as synonymous with conditional. It may be 
necessary to inform the learner also, that hypothetical, in the present accepta- 
tion of the term, are not treated of by Aristotle. They were first sketched by 
Theophrastus, and afterwards more fully developed by Eudemus and the Stoics. 
— [See Mansel, App. p. 57.] 



184 MANUAL OF LOGIC. 

Here both of the parts are true ; yet as the latter does not 
follow from the former, the proposition, as a whole, is false. 
The rules of conditional propositions are three — 

1. If the antecedent is granted, the consequent may be 
inferred. 

2. If the consequent is denied, the antecedent may be 
denied. 

3. Nothing can be inferred either from taking away the 
antecedent, or granting the consequent. 

This arises from the circumstance, that the same consequent 
may follow from another antecedent, although not from that 
from which it is sought to be inferred in some particular 
instance. 

4. Adversative Propositions. 

An adversative proposition is one in which the parts are 
joined by an adversative particle ; as, but, yet, &c, e. g. — 

Travellers may change their climate, but not their dispo- 
sitions. 

Hannibal was a great general, yet finally unfortunate. 

The only difference between a copulative and an adversa- 
tive proposition is, that the adversative particle implies some 
degree of contrariety ; for if we say, 

Anacharsis was a Scythian and a philosopher, 

the proposition is a copulative one ; but if we say, 

Anacharsis was a Scythian, yet a philosopher, 

the proposition is adversative, as it indicates that the terms 
' Scythian ' and ' philosopher ' are not generally predicates 
of the same subject. 

Adversative propositions are sometimes called discretives. 



MANUAL OF LOGIC. 185 

5. Relative Propositions. 

A relative proposition is one whose parts are connected by 
a particle expressing relation ; as, 

Books are valuable, in so far as they are useful. 

6. Causal Propositions. 

A causal proposition is one whose parts are connected by a 
particle asserting that one of them is the cause of the other; as, 

Caesar defeated Pompey, because his army was better dis- 
ciplined. 

Or indicating that one of them is not the cause of the other ; 
as, 

All events are necessary, because they were decreed by fate. 

A causal proposition is contradicted by denying the causa- 
tion. 

7. Comparative Propositions. 

A comparative proposition is one which expresses the 
agreement or disagreement of a predicate and subject with 
each other in a greater or less degree ; as, 

The Greeks were more polished than the Romans. 
The Christian religion is preferable to the Mahometan. 

8. Exclusive Propositions. 

An exclusive proposition is one which asserts that the pre- 
dicate so agrees with the subject as to agree with it only; a as, 

Victoria alone is Queen of England. 

The Platonists were the only school of philosophers who 
maintained the immortality of the soul. 

a There is a difference between the words alone and only, for ' only ' im- 
plies that there is no other of the same kind, while ' alone ' imports being un- 
accompanied with any other. 



186 MANUAL OF LOGIC, 

Exclusive propositions are false, if the predicate does not 
agree with the subject, or if it agrees with more subjects than 
one. 

9. Exceptive Propositions. 

An exceptive a proposition is one which expresses the 
agreement or disagreement of the subject with the predicate, 
except in some part of it ; as, 

All except the wise men are mad. 
All but the pious are foolish. 

The falsehood of an exceptive proposition is shown in the 
same way as in an exclusive. 

10. Inceptive and Desitive Propositions. 

Inceptive and desitive b propositions are those in which 
something is said to begin or end ; as, 

After the death of the Gracchi, Rome ceased to be free. 



SECTION IV. 

CONDITIONAL SYLLOGISMS. 

A syllogism is said to be conditional when either its major 
or minor premiss is expressed under a condition, or both the 
major and minor. 

a An exclusive proposition may be changed into a synonymous exceptive, 
and in the change the subject of the exclusive becomes the excepted part of 
the exceptive. If the exclusive be affirmative, the exceptive will be negative, 
and vice versa, for an affirmative exclusive asserts that the predicate agrees 
with the subject alone, which is the same thing as to say, that tbe predicate 
disagrees with all except that subject; and this is a negative exceptive. Thus 
the exclusive — ' Men are the only animals that reason' — when expressed in the 
form of an exceptive, will be, ' No animals but men reason.' — Walker, p. 80. 

b An inceptive becomes desitive by using the desitive verb for the incep- 
tive, and instead of the state after, the change declaring the state before, and 
similarly the desitive may become inceptive. — Walker, p. 80. 



MANUAL OF LOGIC. 187 

Conditional syllogisms are consequently of three kinds : — 

1. When one of the premisses is conditional, and the con- 
clusion absolute. In this case the major must be the condi- 
tional proposition. 

2. When one of the premisses is conditional and the con- 
clusion conditional. In this case the minor must be the con- 
ditional proposition. 

3. When both major and minor propositions are conditional. 
In this case the conclusion must also be conditional. 

When the major proposition is alone conditional, the con- 
clusion is absolute, for this reason, that in the minor the part 
which asserts or denies the condition is put absolutely, and 
thus prevents the condition from entering the conclusion. 

In conditional syllogisms of this kind, legitimate conclusions 
may be obtained in two ways : — 

1. From the position of the antecedent to the position of 
the consequent, e. g. — 

If the Christian miracles are credible, the Christian doc- 
trines are true ; 

But the Christian miracles are credible ; therefore, 
The Christian doctrines are true. 

In this example we proceed from the position of the ante- 
cedent to the position of the consequent. An argument of 
this kind is said to be constructive, or as it is technically 
/termed in the modus jwnens. 

2. From the remotion of the antecedent to the remotion of 
the consequent, e. g. — 

If Atheists are in the right, then the world exists without a 
cause ; 

But the world does not exist without a cause ; therefore, 
Atheists are not in the right. 

In this example we proceed from the remotion of the con- 
sequent to the remotion of the antecedent. An argument of 



188 MANUAL OF LOGIC 

this kind is said to be destructive, or, as it is technically 
termed, in the modus tollens. 

The conclusiveness of each of these processes of reasoning 
is obvious. In the former example it is asserted in the major, 
that the consequent follows from the antecedent, ,and conse- 
quently, if the antecedent be true, the consequent must be 
true. In the latter example, the consequent is denied, or, in 
other words, is not true ; and hence the antecedent from 
which it follows cannot be true. 

In examples like the foregoing, where the major alone is 
conditional, we must consider the minor as the true proposi- 
tion, for it is absolutely posited ; and the conclusion, there- 
fore, depends for its truth on the truth of the minor. 

It may be remarked, that the removal of the antecedent or 
consequent does not merely signify the denial of it ; but the 
contradiction* of it, for the mere denial of it by a contrary 
proposition, will not make a true syllogism, e. g. — 

If every creature is reasonable, every brute is reasonable ; 
But no brute is reasonable ; therefore, 
No creature is reasonable. 

But if we put the minor in this form, viz., 
Every brute is not reasonable, 
then it will follow legitimately in the conclusion, that 
Every creature is not reasonable. 

It may be remarked, also, that when the antecedent and 
consequent are negative, they are removed by an affirmative, 
as — 

If there be no God, then the world does not exhibit crea- 
tive wisdom; 

a If the absolute premiss assert the falsehood of the consequent, we must 
take care to make the conclusion the contradictory, not the contrary of the 
antecedent. For we can only infer that the antecedent is false, but are not 
thence warranted to assert the truth of its contrary. — Walker's Commentary. 



MANUAL OF LOGIC. 189 

But the world does exhibit creative wisdom ; therefore, 
There is a God. 

But while, in conditional syllogisms of this description, there 
are two legitimate modes of reasoning, there are also two ille- 
gitimate modes, — 

1. When we proceed from the remotion of the antecedent 
to the remotion of the consequent. 

In illustration, let us take the following example : — 

If Mahometanism be true, idolatry is sinful ; 
But Mahometanism is not true ; therefore, 
Idolatry is not sinful. 

It is clear that in this example we cannot proceed from the 
remotion of the antecedent to the remotion of the consequent, 
for the sinfulness of idolatry is not affected by the truth or 
non-truth of Mahometanism. 

2. When we proceed from the position of the consequent 
to the position of the antecedent. 

In illustration, let us take the following example : — 

If states have great standing armies, they are powerful. 
But this state is powerful ; therefore, 
This state has great standing armies. 

It is obvious that in this example we cannot proceed from 
the position of the consequent to the position of the antece- 
dent for great standing armies do not necessarily prove the 
internal power of a state. 

When the subject of the antecedent and consequent is the 
same, a conditional syllogism may be changed into a categori- 
cal one, e. g. — 

If Caesar be a king, he must be honoured ; 
But Caesar is a king ; therefore, 
He must be honoured : 



190 MANUAL OF LOGIC. 

and this syllogism may be changed into a categorical, thus, 

Every king must be honoured ; 
But Caesar is a king ; therefore, 
He must be honoured. 

It has been stated above that when the major alone is con- 
ditional, the conclusion is absolute or categorical ; but w hen 
the minor is conditional, the conclusion is conditional, e. g. — 

The worshippers of images are idolaters. 
If the Romanists worship a crucifix, they are worshippers 
of an image ; therefore, 

If the Romanists worship a crucifix, they are idolaters. 

Syllogisms in which both the major and minor propositions 
are conditional, are best suited to a conditional or hypothetical 
sorites. 

DISJUNCTIVE SYLLOGISMS. 

A disjunctive syllogism is one whose major premiss is dis- 
junctive, and affirmative in quality. 

The parts of a disjunctive syllogism are assumed to contain 
all the possible assertions that can be made regarding the 
subject. 

1. The major premiss must consist of at least two members. 
In this case the minor either asserts the one and the conclu- 
sion denies the other, or the minor denies the one and the 
conclusion asserts the other. 

In a disjunctive syllogism, therefore, we either draw a con- 
clusion from the position of one part to the remotion of the 
other, or from the remotion of one part to the position of the 
other, e. g. — 

The objects in nature either had a commencement, or they 
are self-existent ; 

But they had a commencement ; therefore, 
They are not self-existent. 



MANUAL OF LOGIC. 191 

In this example we draw a conclusion from the position of 
one part to the remotion of the other. 
Again, 

The objects in nature are either self-existent, or were created 
by a self- existent being ; 

But they are not self-existent ; therefore, 
They were created by a self-existent being. 

In this example we draw a conclusion from the remotion of 
the one part to the position of the other. 

2. When the major consists of more than two members, 
either the minor denies some one of them, and the conclusion 
asserts the truth of the rest, or the minor asserts the truth of 
some one of them, and the conclusion denies the rest, e. g. — 

All virtues are either faculties, passions, or habits ; 
But the virtues are neither faculties nor passions ; there- 
fore, 

The virtues are habits. 

In this example the minor denies two of the suppositions, 
and the conclusion asserts the truth of the third. 
Again, 

The sciences arose either from intuition, inspiration, or ex- 
perience ; 

But they arose from experience ; therefore, 

The sciences did not arise from intuition or inspiration. 

In this example the minor asserts or posits the truth of one 
of the 'suppositions, and the conclusion denies the other two. 

Disjunctives may be resolved into conditionals, by altering 
the form of the major premiss, i. e., changing the disjunctive 
particles into conditional, e. g. — 

The objects in nature are either eternal, or the results of 
chance, or the eiFects of intelligent agency ; 



192 MANUAL OF LOGIC. 

But they are neither eternal, nor the results of chance ; 
therefore, 

They are the effects of intelligent agency. 

This example, reduced to the conditional form, is as fol- 
lows : — 

If the objects in nature are neither eternal, nor the results 
of chance, they are the effects of intelligent agency ; 

But they are neither eternal nor the results of chance ; 
therefore, 

They are the effects of intelligent agency. 

Here the same minor and conclusion equally apply. 



SECTION" V. 



OF THE DILEMMA. 



The dilemma a is a conditional syllogism, with a disjunctive 
antecedent or consequent. It partakes both of the conditional 
and disjunctive argument. 

In the conditional premiss of a dilemma, either the antece- 
dent or consequent may be disjunctive. 

A dilemma may prove either an affirmative or negative 
conclusion. 

When an affirmative is proved, the dilemma is said to be 
in the modus ponens ; when a negative is proved, it is said to 
be in the modus tollens ; when the conclusion is in the 
modus ponens, the argument is said to be constructive ; and 

a The word dilemma means ' double proposition ;' so that the whole argu- 
ment takes its name from the one mixed judgment in it. When this is more 
than double, as in, ' If a prisoner is legally discharged, either the magistrate 
must refuse to commit, or the grand jury ignore the will, or the common jury 
acquit, or the crown exercise the prerogative of pardon,' the argument has been 
called a trilemma, tetralemma, or polylemma, according to the number of mem- 
bers the judgment may have. — Outlines of the Laws of Thought, p. 286. 



MANUAL OF LOGIC. 193 

when in the modus tollens, destructive. A dilemma is said 
to be simple when it concludes categorically, and complex 
when its conclusion is disjunctive. 

A dilemma is an argument by which we endeavour to 
prove the absurdity or falsehood of some assertion. With 
this view, a conditional proposition is assumed, the antece- 
dent of which is the assertion to be disproved, while the con- 
sequent is a disjunctive proposition, enumerating all the 
possible suppositions upon which the assertion contained in 
the antecedent can be true. Should all the suppositions con- 
tained in the consequent be rejected, it must follow that the 
antecedent must also be rejected. If, therefore, a proposition 
of which the antecedent is conditional, and the consequent 
disjunctive, be the major of a syllogism, and if the minor 
deny all the suppositions enumerated in the consequent, it 
will follow necessarily that the conclusion must deny the 
antecedent. 

In the strictest form of the dilemma, it is supposed that 
some one of the antecedents must be true, or some one of the 
consequents false ; but without determining which of them is 
so. The name dilemma also refers to the circumstance, that 
the major, in stating the argument, presents two suppositions 
or cases from each or both of which the same conclusion may 
be drawn. 

Certain kinds of dilemmas require, as will be, seen from the 
following examples, that the denial of each branch of the 
consequent must be proved in the minor by a prosyllogism, 
e. g — 

If there are two independent first principles, the one good 
and the other evil, either the one is more powerful than the 
other, or they are equal in power. a 

But the one is not more powerful than the other ; (for if it 
it were, it would entirely prevent the other from having any 

a Arthur's Essay on ' Evils and their Causes.' 

I 



194 MANUAL OF LOGIC. 

share in the production or government of the universe : and 
therefore everything would be either absolutely good or abso- 
lutely evil.) Neither are they equal in power; (for if they were, 
but had opposite wills, they would counterbalance each other, 
and therefore produce nothing.) 

Therefore, there are not two independent first principles, 
the one good and the other evil. 

In this dilemma, the antecedent is the assertion to be dis- 
proved by remotion. All the suppositions enumerated in the 
disjunctive part of the major, on which the antecedent could 
be tenable, are removed in the minor by means of proofs pro- 
syllogisticalrv attached ; and, as a necessary consequence, the 
conclusion rejects the antecedent. 

This dilemma may be reduced to the two following condi- 
tional syllogisms : — 

1. If there are two independent first principles, the one 
more powerful than the other, everything would either be 
absolutely good or absolutely evil. 

But the present is not the case of everything being either 
absolutely good cr absolutely evil. 

Therefore, there cannot be two independent first principles, 
the one more powerful than the other. 

2. If there are two independent first principles, equal in 
power but of opposite wills, they must counterbalance each 
other, and produce nothing. 

But the present is not the case of nothing being produced. 
Therefore, there are not two independent first principles 
equal in power, but of opposite wills. I 

The following example is of a simpler character : — 
If perfect virtue exists, it exists either among civilised or 
among uncivilised communities. 

But perfect virtue cannot exist among civilised commu- 
nities ; (for civilisation produces only a spurious kind of 



MANUAL OF LOGIC. 195 

virtue, inclining rather to expediency than rectitude.) Neither 
can it exist among uncivilised communities ; (for the actions 
of savages are regulated by narrow selfishness, which is in- 
compatible with perfect virtue.) 

Therefore, perfect virtue does not exist. 

The simple constructive dilemma has a major premiss, con- 
taining several antecedents, with one common consequent, 
and a minor which grants these antecedents disjunctively, 
i. e., grants some one of them, e. g. — 

If the heavenly inhabitants have either no desires, or have 
these fully gratified, they are perfectly happy. 

But they either have no desires, or have them fully 
gratified. 

Therefore, they are perfectly happy. 

If a Christian be living, he is the Lord's servant ; and if he 
be dead, he is the Lord's servant. 

But he must be always either living or dead. 
Therefore, he is always the Lord's servant. 

In a constructive dilemma, some one of the antecedents is 
assumed to be true ; and in a destructive, some one of the 
consequents is assumed to be false, but which is left unde- 
termined. 

The complex constructive dilemma has a major premiss, 
containing several antecedents, each with a different conse- 
quent, and a minor which grants the antecedents disjunc- 
tively ; while the conclusion infers the consequents disjunc- 
tively, i. e., determines one of them to be true, e. g. — 

If the evangelists speak truth, Christianity is of God ; and 
if they do not speak truth, the existence of Christianity is 
unaccountable. 

But the evangelists either do or do not speak truth. 

Therefore, Christianity is either of God, or its existence is 
unaccountable. 



196 MANUAL OF LOGIC. 

The destructive* dilemma has a major, containing several 
antecedents, each with a different consequent, and a minor 
denying the consequents disjunctively ; while the conclusion 
also disjunctively denies the antecedents, e. g. — 

If men were wise, they would avoid speaking irreverently 
of sacred things, even in jest ; and if they were good, they 
would avoid doing so in earnest. 

But many do not avoid this, either in jest or earnest. 

Therefore, many are either not wise or not good. 

If a witness be an honest one, he will not bear false testi- 
mony designedly ; and if he be a competent one, he will not 
do so undesignedly. 

But a witness who speaks false, does so either designedly 
or undesignedly. 

Therefore, he is either not honest or not competent. 

The facility with which a destructive dilemma may be 
reduced to two conditional syllogisms, may be seen from the 
following example, viz., — 

If this man were prudent, he would behave well for his 
own sake ; and if he were benevolent, he would behave well 
for the good of others. 

But he does not behave well, either for his own sake or the 
good of others. 

Therefore, he is neither prudent nor benevolent. 

1. 

If this man were prudent, he would behave well for his 



a Whateley and others seem to be of opinion, that a destructive dilemma, 
properly so called, should, like the complex constructive, have a disjunctive 
minor premiss; and this they term the only true form of the destructive 
dilemma. In point of fact, however, the simple destructive is a still more com- 
mon form, and any arguments adduced against it will equally apply to the 
simple constructive. 



MANUAL OF LOGIC* 197 

But he does not behave well for his own sake. 
Therefore, he is not prudent. 

2. 

If this man were benevolent, he would behave well for the 
good of others. 

But he does not behave well for the good of others. 
Therefore, he is not benevolent. 

A dilemma may become invalid in one or other of three 
ways. 

1. When the members of the division in the disjunctive 
part of the major are not adequate to the whole divided; in 
other words, when they do not enumerate all the possible 
suppositions, e. g. — 

If a writer is to be accounted original, it must either be in 
virtue of innate ideas, or of thoughts taken from other 
authors. 

But a writer cannot be accounted original in virtue of in- 
nate ideas ; (for if ideas are innate, they are common to men 
in general;) neither can he be accounted original, if his 
thoughts are taken from other authors ; (for in this case he is 
a plagiarist.) 

Therefore, in no case can a writer be accounted original. 

In this example, it is evident that in the disjunctive part of 
the major an alternative is omitted, viz., that a writer may 
have ideas which are peculiarly the product of his own in- 
tellect, and which consequently are neither innate nor taken 
from other writers. 

If Abraham were justified, it must have been either by faith 
or by works. 

Now he was not justified by faith (according to James,) nor 
by works (according to Paul.) 

Therefore Abraham was not justified. 



198 MANUAL OF LOGIC. 

In this example the alternative — by faith and works 
conjointly is omitted. 8 

2. If the prosyllogistic proof is insufficient to prove the 
minor, e. g. — 

If the soul be annihilated, it must be by something which 
is in existence, or something which is not. b 

But that which is in existence can never produce what is 
physically contrary to itself; and that which has no existence, 
cannot act. 

Therefore, the soul cannot be annihilated. 

That the proof of the minor fails will be readily seen by 
reducing the argument to two conditional syllogisms ; thus — 

1. 

If the soul can be annihilated by something which exists, 
that something must produce what is physically contrary to 
itself. 

But no existence can produce what is physically contrary 
to itself. 

Therefore, the soul cannot be annihilated by anything 
which exists. 

2. 

If the soul can be annihilated by something which does 
not exist, that something must act. 

But that which does not exist cannot act. 

Therefore, the soul cannot be annihilated by that which 
does not exist. 

Two objections may be made to the part of the minor, 
which asserts that what is in existence cannot produce any- 
thing physically contrary to itself. 1. The asserted impos- 

a Considering logic as a formal science, the supplying of an omitted alterna- 
tive is a material, not a logical merit. 

b Drew's Essay on the Immortality of the Soul. 



MANUAL OF LOGIC. 199 

sibility is merely an assumption ; and, 2. If the Omnipotent 
can create out of nothing, a greater exertion of power is not 
required to annihilate what has been so created. 
But to take a simpler example, viz. — 

If a man study metaphysics, he must either follow implicitly 
some existing works on the subject, or he must trace the 
workings of his own mind. 

But if he follows implicitly some existing works on the 
subject, he must take his knowledge from authority ; and if 
he traces the workings of his own mind, he will involve him- 
self in inextricable confusion. 

Therefore, he must either take his knowledgefrom auth o- 

rity, or involve himself in inextricable confusion. 
i 
In this argument the second alternative does not hold true ; 

for a man may trace the workings of his own mind without 

involving himself in inextricable confusion. 

3. A dilemma ought to be incapable of being retorted. 

The retortibility of a dilemma is rather a mark by which 
we may conclude it to be fallacious, than any distinct circum- 
stance of invalidity. 

The following example is, in substance, taken from one of 
Cicero's letters to a provincial dignitary who had upbraided 
him for negligence in his correspondence. 

If your letters have ceased, you have either become lazy, 
or you do not value my friendship, or you have forgotten me. 

But your letters have ceased. 

Therefore, you have either become lazy, or you do not value 
my friendship, or you have forgotten me. 

This dilemma is vitiated by an illogical distribution of the 
major premiss for the supposition, ' or your attention is other- 
wise engrossed/ is omitted. Instead of pointing out the logical 
inaccuracy, Cicero retorts the dilemma, as they were both 
equally dilatory in their correspondence. 



200 MANUAL OF LOGIC. 

There is a well-known ancient example of a retortible 
dilemma mentioned by Anlus Gellius, and generally quoted 
by logicians, which may be added: — 'Euathlus, a rich young 
man, desirous of learning the art of pleading, applied to Pro- 
tagoras, a celebrated sophist, to instruct him, promising a 
great sum of money as his reward, one-half of which was paid 
down, the other half he bound himself to pay as soon as he 
should plead a cause before the judges and gain it. Prota- 
goras found him a very apt scholar ; but after he had made 
good progress, he was in no haste to plead causes. The 
master, conceiving that he intended, by these means, to shift 
off his second payment, took, as he thought, a sure method of 
getting the better of his delay. He sued Euathlus before the 
judges ; and, having opened his cause at the bar, he pleaded 
to this purpose : — " O most foolish young man, do you not see 
that, in any event, I must gain my point ? for, if the judges 
give sentence for me, you must pay by their sentence ; if 
against me, the condition of our agreement is fulfilled, and 
you have no plea left for your delay, after having pleaded and 
gained a cause." To which Euathlus answered, " O most 
wise master, I might have avoided the force of your argu- 
ment by not pleading my own cause. But, giving up this 
advantage, do you not see that, whatever sentence the judges 
pass, I am safe ? If they give sentence for me, I am acquitted 
by their sentence ; if against me, the condition of our agree- 
ment is not fulfilled by my pleading a cause and losing it.'" 

The dilemma, as used by Protagoras, maybe thus stated : — 

Either the cause will go on my side, or on yours. 

If the cause goes on my side, you must pay me according 
to the sentence of the judge ; if the cause goes on your side, 
you must pay me according to your bargain. 

Therefore, whether the cause goes for me or against me, 
you must pay me the reward. 

Euathlus retorted the dilemma thus : — - 



MANUAL OF LOGIC. 201 

Either I shall gain the cause, or lose it. 

If I gain the cause, then nothing will be due to you, ac- 
cording to the sentence of the judge ; but if I lose the cause, 
nothing will be due to you, according to my bargain. 

Therefore, whether I gain or lose the cause, I will not pay 
you, for nothing will be due to you. a 



SECTION VI. 

OF THE ENTHYMEME. b 

A very prevalent error, regarding the nature of the entby- 
meme, is, that it is a syllogism with one premiss suppressed, 

a This story is by the Greek authors generally told of the Rhetorician Corax 
(crow) and his pupil Tisias. The puzzled judges, in lieu of a decision in the 
case, angrily pronounced of plaintiff and defendent — Kaxov 7tooa7iog xolkov 
ojov (plaguy egg of a plaguy crow I) Hence the proverb. — Sir W. Hamilton 
Reid's Works, p. 704. 

The dilemma of Bias, viz. — Si uxorem ducas formosam, habebis communem, 
se deformem, psenam : ergo Nulla est ducenda — like many other examples, may 
be shown to be false, from not enumerating all the possible suppositions ; for 
as Aldrich observes, i est qucedam media pulchritudo, — (there is a certain inter- 
mediate degree of beauty,) or it may be shown to be retortible ; thus :— 

Si formosam duxero, non habebo psenam : si deformem, non habebo com- 
munem. 

b The usual view of the enthymeme, though of a remote date, is not Aristotelic. 
The Stagirite, as mentioned in the text, distinguishes the enthymeme from the 
pure syllogism by considering it as a reasoning of a peculiar matter, a reasoning 
proceeding on signs or likelihoods, 6vKkoyi<S(j,og (arihy\q) s|j sixoruv r\ 
<frjfjbSiC/JV. The term ar sXyjg (imperfect), usually introduced into this defini- 
tion, and on which the common view of the enthymeme mainly rests, has been 
ejected as spurious, en the most satisfactory authority. The supposition, also, 
that the word svdvfjbyi/ua, from being compounded of sv and du/nog, which, 
in an etymological point of view, is certainly correct, has tended much to 
confirm the general misapprehension. In the language of Aristotle, 6v(x,oc 
is not the mind; neither does he use the word svduftYjftCC as having anything 
to do either with expressed or suppressed premisses. Other writers also used 

i2 



202 MANUAL OF LOGIC. 

or, as it is often termed, an imperfect or defective syllogism. 
In Aristotle's writings, it never means this. The term im- 
perfect is not applied by him to an argument with a sup- 
pressed premiss, but to a syllogism drawn in the second 
or third figure, the truth of which is not directly evident by 
the dictum de omni et de nullo. 

An enthymeme, in its proper signification, may be as com- 
plete in its expression as any other kind of syllogism ; for it 
merely differs from the syllogism in this, that its conclusion 
depends on signs and likelihoods, 9. Its province is mainly 
probable reasoning, and therefore treats reasoning as applied 
to a particular kind of matter. It does not proceed upon 
axioms, like the syllogism. The matter of the major pre- 
miss of an enthymeme is taken from the two/ (topics or com- 
mon places), and these hold the same place in regard to the 
enthymeme, which the axioms do to the syllogism. The 
ronoi, or common places, are general principles, based on 

the word, but without any technical significance. The following passages from 
Sophocles may suffice in proof of this : — 

rapfiuv fjjiv o) yiQcuz ravdu/jb^fiara croXX?j tfr avctyxv) raito gov. 
— (Ed. Col. 292. (Much and forcible reason is there to be awed by the 
sentiments uttered by thee, old man.) 

g % 2/ £ 7 a i ou X l fiuiM rav&v[LYi{LaTa tojv tfwv adsgxrwv ofL^aruv 
ryjTWfASVog. — Ibid, 1199. (For you bear no slight impressions of this, being 
deprived of your sightless eyes.) 

It would appear from these passages, that the word zv&v^fia originally 
meant something present to the mind for consideration or reflection ; and the 
transition from this, as Mr Mansel observes, to an argument of probability — a 
suggestion, though not demonstrative, yet deserving attention in practical ques- 
tions — is easy and natural enough. On this point the learner may advanta- 
geously consult Ed. Rev., vol. lvii., p. 221 ; Mansel, app. p. 40, et seq. 

a E//torc« — 2^/xs/a — Tzx/UYigiov. 'An argument which alleges some 
antecedent, is called by Aristotle an eixog ; and that which alleges some con- 
sequent, a (fvjfisiov. If it alleges a consequent which could not have been 
produced by any other cause but the supposed one, the argument is a rsx/Migiov, 
or positive proof. For instance, if it is to be proved that A murdered B, any 
former grudge of A's against B would be an sixog, or predisposing cause 
which might have produced the act ; and any sudden enrichment of B just 
about the time of the murder, would be a tfTj/xs/ov, or probable effect of the 
action.' — Molerly, p. 166. 



MANUAL OF LOGIC 203 

probabilities, not on axioms ; and the term swoc, in this ap- 
plication, may be explained by naming it the place where 
middle terms are found. a But since en thym ernes derive their 
force only from cumulation, there is nothing gained from 
reducing them to syllogistic form. 

The foregoing is a brief statement of the nature of the 
Aristotelian enthymeme, and is merely given to guard the 
learner against a prevalent, though erroneous notion. The 
common view, however, whether the result of misapprehension 
or of intentional innovation, has been too long countenanced 
by almost all writers on logic to be readily rejected. It is a 
question, indeed, how far the rejection of the common view is 
desirable, if we consider how much it conduces to logical 
expertness. In ordinary argumentation, syllogisms invari- 
ably occur in an abbreviated form, for the entire statement of 
premisses and conclusion would appear pedantic and artificial ; 
and in connection with the word enthymeme, in its ordinary 
acceptation, it may not be out of place to lay before the learner 
the rules by which he may ascertain the particular figure in 
which any enthymeme may be drawn . b 

An enthymeme, as commonly defined, is an irregular syllo- 
gism in which one of the premisses is suppressed, or, as it 
might be, more properly defined — an argument in the form in 

a Quum pervestigare aliquod volumus locos nosse debemus : sic enim ap- 
pellate sunt hse quasi sedes e quibus argumenta promuntur. Itaque licet 
definire locum esse argumenti sedem ; argumentum autem, rationem, quae rei 
dubise faciat fidem ; Cic. Top. cap. 2. — (When we wish to trace out any argu- 
ment, we ought to know the places, for, on this account, they have been named 
by Aristotle the seats, as it were, whence arguments are adduced. Therefore, 
we may define a place to be the seat of an argument, but an argument the reason 
or cause which confirms something doubtful.) The word argument is used here 
as synonymous with the middle term. 

b In the formal view of logic, the enthymeme cannot be considered as syllo- 
gistic, for our belief in its conclusiveness must arise from our knowledge of 
the object-matter, and without this knowledge we could not supply the sup- 
pressed premiss either actually or mentally. 



204 MANUAL OF LOGIC. 

which it would naturally occur in thought or speech. It con- 
sequently consists of only the expressed premiss and the con- 
clusion. These are designated the antecedent and consequent, 
the latter being the conclusion of the syllogism, and the 
former either the major or minor premiss. 

Although the enthymeme, as ordinarily understood, is a 
defective syllogism, consisting of only one premiss and the 
conclusion, it always implies a syllogism, and expresses its 
terms. 

If the syllogism implied in an enthymeme be a simple one, 
it will be easy to discover which of the premisses has been 
suppressed, by observing which of the extremes occurs in it ; 
because one or other of the extremes must occur in each pre- 
miss, and from this we ascertain which of the premisses the 
antecedent is, and how the syllogism is to be completed. 

One of the terms (viz. one of the extremes of the question) 
always occurs twice, and when this term is the subject of the 
consequent, the major premiss is suppressed ; but if the term 
twice occurring be the predicate of the consequent, the minor 
premiss is suppressed. The suppressed premiss is supplied 
by comparing with the middle term the extreme which occurs 
only once. a 

In the greater number of enthymemes the minor is ex- 
pressed as being more particularly related to the question to 
be proved, and also as being more likely to be called in ques- 
tion than the major. The major, as already stated, is usually 

Although the major premiss is generally suppressed in most enthymemes, 
yet there are some enthymemes in which the minor premiss is found to be 
omitted. This may happen when the minor premiss is very evident, or when 
much stress is meant to be laid upon the major, e. g. — « Every tyrannical king 
deserves to be deposed by his subjects ; therefore, Nero deserved to be deposed 
by the Romans.' The minor premiss which is suppressed may be thus sup- 
plied — 

' Nero was a tyrannical king ;' 

and thus the argument is reduced to regular syllogistic form. — Huyshe, p. 129. 



MANUAL OF LOGIC. 205 

of a more general character than the minor, containing a truth 
better known, and consequently less liable to objection or 
contradiction. 

In order to show in what figure an enthymeme is drawn, 
the following rules have been laid down ; and by attending 
to these, in connection with the special rules of syllogisms, 
the figure of an enthymeme may be readily ascertained. 

Rule I. 

When the antecedent and consequent have a common sub- 
ject, the enthymeme is drawn either in the first or second 
figure, and the major premiss is suppressed. 

Here three thiugs are to be noted. 

1. That it is only in the first and second figures that the 
minor proposition and conclusion can have a common subject. 

2. That if the minor is negative, the enthymeme is not 
drawn in the first figure. 

3. That if the conclusion is affirmative, the enthymeme is 
not drawn in the second figure. 

In the following enthymeme, viz. : — 

Isaiah was a true prophet ; therefore, 
Isaiah was inspired, 

the antecedent and consequent have a common subject, viz. 
' Isaiah.' The other terms are ' prophet,' the predicate of the 
antecedent, and ' inspired' the predicate of the consequent; 
but since a syllogism can only have three tei ms, and as the 
middle term does not appear in the conclusion, the term 
1 prophet' must be the middle term ; and by comparing it dis- 
tributed with the major term ' inspired,' we supply the sup- 
pressed premiss, and have a syllogism in Barbara of the first 
figure. Thus, 

All true prophets are inspired. 
Isaiah was a true prophet. 
Isaiah was inspired. 



206 MANUAL OF LOGIC. 

The following enthymeme, viz. : — 

1 No guilty pleasures are unattended with remorse, there- 
fore no guilty pleasures are truly satisfactory,' 

is drawn in the second figure. The consequent and the ante- 
cedent have a common subject, viz. ' No guilty pleasures ;' the 
other terms being ' truly satisfactory,' and ' unattended with 
remorse,' which latter term must be the middle, as it does not 
appear in the conclusion ; and by comparing it with the major 
term ' truly satisfactory,' we supply the suppressed premiss, 
and have a complete syllogism in Camestres of the second 
figure. Thus, 

Whatever is truly satisfactory is unattended with remorse. 
No guilty pleasures are unattended with remorse. 
No guilty pleasures are truly satisfactory. 

Rule II. 

When the antecedent and consequent have a common pre- 
dicate, the enthymeme is drawn either in the first or third 
figure, and the minor is suppressed. 

It must be noted here, — 

1. That it is only in the first and third figures that the 
major proposition and conclusion can have a common predicate. 

2. That if the conclusion is universal, the enthymeme is not 
drawn in the third figure. 

In the following example, viz. : — 

Nothing difficult of attainment is within reach of the indo- 
lent ; therefore, useful knowledge is not within reach of the 
indolent, 

the antecedent and consequent have a common predicate, viz. 
' within reach of the indolent ;' and, as the only other term 
which does not appear in the conclusion is l nothing difficult of 
attainment,' this must be the middle term ; and by comparing 
it with the subject of the conclusion, viz. ' useful knowledge,' 



MANUAL OF LOGIC. 207 

we supply the minor premiss, and have a complete syllogism 
in Celarent of the first figure. Thus, 

Nothing difficult of attainment is within reach of the indo- 
lent. 

All useful knowledge is difficult of attainment ; therefore, 
Useful knowledge is not within reach of the indolent. 

The following enthymeme, viz. : — 

All who believe in dreams, must be ignorant of the effects 
produced by external objects on the body in sleep ; therefore, 
some ancient poets must have been ignorant of the effects pro- 
duced by external objects on the body in sleep, 

is in the third figure ; and by comparing the subject of the 
consequent or minor term, viz., ' some ancient poets,' with the 
middle term, ' believe in dreams/ we supply the minor pre- 
miss, and have a regular syllogism in Datisi. Thus, 

All who believe in dreams must be ignorant of the effects 
produced by external objects on the body in sleep. 

Some who believed in dreams were ancient poets. 

Some ancient poets must have been ignorant of the effects 
produced by external objects on the body in sleep. 

KULE III. 

When the subject of the antecedent is the predicate of the 
consequent, the enthymeme is drawn either in the second or 
fourth figure, and the minor is suppressed. 

It must be observed here, — 

That it is only in the second and fourth figures that the 
subject of the major proposition can be the predicate of the 
conclusion. 

An enthymeme is frequently an abbreviation of a condi- 
tional or disjunctive syllogism, and in either of these cases it 
presents four different terms, neither of which occurs twice. 
JBut as the consequent, in such circumstances, depends alto- 



208 MANUAL OF LOGIC. 

gether on the suppressed premiss, that premiss must be 
either a conditional or disjunctive major proposition, e. g — 
* The objects in nature are not self- existent. Therefore, they 
were created by a self-existent being.' This example, on 
examination, will prove to be a conditional syllogism in an 
abbreviated form, and may be expanded thus, — . 

If the objects in nature are not self-existent, they were 
created by a self-existent being. 

But the objects in nature are not self-existent ; therefore, 
They were created by a self- existent being. 



SECTION VII. 

OF THE EPICHEIREMA. 

An Epicheirema a is a syllogism, with a prosyllogism ap- 
pended either to the major or minor premiss, or to both. 
The prosyllogism is incidentally introduced, with the view of 
proving one or other of the premisses of the argument laid 
down. It forms the expressed premiss of an enthymeme, of 
which the premiss to which it is appended is the conclusion, 
e. g.— , 

All sin is dangerous. 

Covetousness is sin, (for it is a transgression of the law ;) 
therefore, 

Covetousness is dangerous. 

The minor premiss, viz. — 

Covetousness is a transgression of the law; therefore, it is sin — 

is an enthymeme. 

The following example of an epicheirema is a syllogistic 
condensation of Mr Payne's refutation of Dr Brown's theory 
on the nafure of virtue. In answer to the questions, What 

a A syllogism with such a premiss is so called from scr/p£S/gsw, I undertake 
to prove. 



MANUAL OF LOGIC. 209 

is virtue ? How do our feelings of moral approbation arise ? 
Dr Brown states that virtue is a relation, and that relations 
do not exist in the objects, but in the mind that contemplates 
them — that there is no virtue in actions — nothing that is in 
one action which does not exist in another, to excite the 
emotion of moral approbation — that virtue is a felt relation to 
certain emotions, and nothing more — that the mind might have 
been formed capable of approving what it now disapproves ; 
and in this case vice would not only seem virtue, but would 
really be virtue, as both depend on the arbitrary constitution 
of the mind. 
Mr Payne's refutation maybe epicheirematically stated thus — 

Whatever theory maintains that virtue has no character of 
itself, but depends on the arbitrary constitution of the mind, 
must be false ; (for it supplies us with no adequate cause for 
the rise of the emotion of approbation ; for it proceeds on a 
practical forgetfulness of the distinction which exists between 
what is and what might to be ; for it implies that the most 
flagitious actions may, upon a change of opinion, not only 
lose all their turpitude, but become positively virtuous ; for it 
implies that we do not approve of an action, because it is 
right, but that the action becomes right, because we approve 
of it.) 

But Dr Brown's theory maintains that virtue has no cha- 
racter of itself, but depends on the arbitrary constitution of 
the mind ; therefore, 

Dr Brown's theory must be false. 

The prosy llogi stic proofs may be stated in separate syllo- 
gisms; thus — 

Every theory on virtue that supplies us with no adequate 
cause for the rise of the emotion of moral approbation must 
be false. 

Every theory on virtue maintaining that it has no 
character of itself, but depends on the arbitrary constitution 



210 MANUAL OF LOGIC. 

of the mind, supplies us with no adequate cause for the rise 
of the motion of moral approbation ; therefore, 

Every theory on virtue maintaining that it has no 
character itself, but depends on the arbitrary constitution 
of the mind, must be false. 

The learner may easily throw the remaining prosyllogistic 
proofs into syllogisms. 

The following examples may be subjoined for exercise. 

One of the best and most frequently quoted examples, is 
Cicero's defence of Milo. It is as follows : — 

He who attempts to assassinate another, may be justly 
killed by the object of his murderous intentions ; (for the laws 
of nature, and of nations, and the conduct of good men, prove 
it lawful.) 

But Clodius attempted to assassinate another ; (for he 
formed an ambuscade against him, and provided himself with 
armed soldiers ;) therefore, 

Clodius was justly killed, by the object of his murderous 
intentions. 

Studies which regulate the conduct of the mind are of the 
utmost importance ; (for it is the mind which directs all our 
actions.) 

Logic is a study which regulates the conduct of the mind ; 
(for it is wholly employed about its operations ;) therefore, 

Logic is a study of the utmost importance. 

This form of reasoning is often employed efficaciously; but 
every superfluous proof should be omitted. In many exam- 
ples, the proof of the minor is of little use ; yet, whenever 
the auxiliary propositions are employed to strengthen either 
the agreement or repugnancy of the extremes in the con- 
clusion, they are used with effect. 



MANUAL OF LOGIC. 211 

SECTION Till. 

OF THE SORITES. 

The sorites a is so named from 6c*jgog, a heap. It consists of a 
series of propositions so arranged, that the predicate of each 
becomes the subject of the next, till at length, in the ultimate 
conclusion, the predicate of the last proposition is affirmed or 
denied, as the case may be, of the first subject in the series. 
In a sorites there are as many middle terms as there are in- 
termediate propositions between the first and last, the subject 
of each intermediate proposition being a middle term. A 
sorites may, therefore, be drawn out into as many separate 
syllogisms as there are intermediate propositions, since each 
intermediate proposition contains a middle term. b 

In this kind of syllogism the mind proceeds from link to 
link in the chain of reasoning, without drawing separate con- 
clusions, as for instance, 

A is B, 

BisC, 

CisD, 

DisE, 
Therefore A is E, 
but for these abstract symbols let us substitute an example. 

The term sorites implies that the propositions are piled, as it were, one 
on another. The German term (kettenschluss), meaning chain-argument, is 
more appropriate, as it denotes the mind's progress in linking one judgment to 
another in a process of argumentation. 

b A sorites has as many middle terms as there are propositions, less by two, 
for there are exaetly as many different terms as propositions, but two of these 
terms are extremes. It hence also appears that if a sorites be resolved into 
syllogisms, those syllogisms will be two less than the propositions of the sorites, 
since there will be as many syllogisms as there are middle terms. However, 
the number of syllogisms may be better determined thus ; if but one proposition 
of the sorites were employed in each syllogism, there would be as many syllo- 
gisms as propositions ; but in the first and last syllogism there are, respectively, 
two propositions of the sorites used, and for each of the intervening syllogisms 
but one proposition. — Walker. 



212 MANUAL OF LOGIC. 

All who truly love wisdom earnestly desire it ; 

All who earnestly desire wisdom use the means of attain- 
ing it ; 

All who use the means of attaining it encounter difficulties ; 

All encountering difficulties are patient, persevering, and 
self- denied ; 

All who are patient, persevering, and self-denied, are vir- 
tuous ; 

Therefore, all who truly love wisdom are virtuous. 

The separate syllogisms into which a sorites may be 
expanded may be all of the first figure, and as the design of 
forming them is to bring the minor extreme, or first term, 
into connection with all the other terms, the following 
arrangement is followed. The first syllogism in the series 
has for its major premiss the second proposition in the 
sorites, and for its minor premiss the first proposition ; while 
the conclusion connects the minor extreme with the second 
middle term, thus — 

All who earnestly desire wisdom use the means of attain- 
ing it ; 

All who truly love wisdom earnestly desire it ; 

All who truly love wisdom use the means of attaining it. 

In the second syllogism, the major premiss is the third pro- 
position in the sorites, and the minor the conclusion of the 
first syllogism, thus — 

All who use the means of attaining wisdom encounter 
difficulties ; 

All who truly love wisdom use the means of attaining it. 
All who truly love wisdom encounter difficulties. 

The same order is followed in the remaining syllogisms — 
the succeeding proposition becoming the major, and the con- 
clusion of the preceding syllogism the minor of each. The 
series ends when the first term in the sorites, or the minor 



MANUAL OF LOGIC. 213 

extreme, is connected, or compared with the last predicate, 
or major extreme, as follows : — 

All who encounter difficulties are patient, persevering, and 
self-denied. 

All who truly love wisdom encounter difficulties. 

All who truly love wisdom are patient, persevering, and 
self-denied. 

All who are patient, persevering, and self-denied, are virtuous. 
All who truly love wisdom are patient, persevering, and 
self-denied. 

All who truly love wisdom are virtuous. 

The true force of the argument in a sorites is to be de- 
duced, not from the resolution of it into syllogisms, but from 
the consideration that something is universally affirmed or 
denied in the last premiss of a term, in which the preceding 
premisses show that the first subject is contained ; and there- 
fore, in the conclusion, the same is legitimately affirmed or 
denied of the first subject, in the same quantity which it has 
in the first premiss. 

It has been stated above, that in expanding a sorites into 
separate syllogisms, the first in the series has for its major 
premiss the second proposition in the sorites, and the first 
proposition for its minor. This transposition is required, in 
order that the separate syllogisms may be in the first figure, 
and consequently brought under the dictum which applies to 
that figure. Thus all the syllogisms will be in the first figure, 
and all except the last will be in the moods AAA or AAI, in 
the latter, if the first premiss of the sorites be particular. On 
examining the two first propositions in the foregoing sorites, 
it will be seen that the middle term is the predicate of the 
major and the subject of the minor ; hence were a conclusion 
to be drawn without a transposition of the premisses, the 
syllogism would be in Bramantip of the fourth figure ; thus — 



214 MANUAL OF LOGIC. 

All who truly love wisdom earnestly desire it. 

All who earnestly desire wisdom use the means of attaining it. 

Some who use the means of attaining it truly love wisdom. 

It has also been stated, that in the second syllogism of an 
expanded sorites, the major premiss is the third proposition in 
the series, and the minor the conclusion of the first separate 
syllogism. And it may be mentioned, in explanation of this, 
that as the two first propositions in the sorites have been made 
use of in the first separate syllogism, in drawing the second 
syllogism, the third proposition in the sorites, used as a major 
premiss, with the conclusion of the first separate syllogism 
used as a minor, will give a conclusion in Barbara of the first 
figure. The process consequently to be followed, in expand- 
ing a sorites into separate syllogisms, is to begin with trans- 
posing the two first propositions in the soritical series, in 
order to give the middle term its proper place in the premisses 
of a syllogism drawn in the first figure ; and, in the second, 
to use the third proposition in the sorites as a major, with the 
conclusion of the first separate syllogism as a minor. This 
latter process is equally necessary as the first, in order to 
bring all the separate syllogisms under the principles which 
regulate the first figure. 

With reference to a categorical sorites, such as given above, 
it may be remarked — 

1. That no proposition of a sorites except the last can be 
negative. 

2. That no proposition of a sorites can be particular ex- 
cept the first. And 

3. That if the first proposition be particular, the conclusion 
must be particular. 

In explanation of the first of these rules, viz., that no pro- 
position except the last can be negative, it may be stated 
that when a sorites is expanded into separate syllogisms, the 
last syllogism can alone admit of a negative premiss and con- 



MANUAL OF LOGIC. 215 

elusion ; for since the middle term is the subject of the major 
proposition, the syllogism must be either of the first or third 
figure, and, consequently, by the special rules applicable to 
these figures, the minor must be affirmative. But the minor 
of each successive syllogism is the conclusion of that preced- 
ing, and, by being affirmative, proves that the premisses from 
which it was deduced were also affirmative. The last pre- 
miss of the sorites, therefore, viz., the last intermediate propo- 
sition, is the only one that can be negative, because the last 
premiss alone never gives occasion to employ the conclusion 
of the last expanded syllogism as the minor of a subsequent 
one ; for should any other premiss of the sorites but the last 
be negative, it would lead to a negative conclusion, and that 
conclusion being made the minor of the following syllogism, 
would violate the special rules of the first, which does not 
admit of a negative minor premiss. 

In explanation of the second of the foregoing rules, viz., 
that no proposition of a sorites can be particular except the 
first, it may be stated that since in expanding a sorites into 
separate syllogisms of the first figure, it is necessary to trans- 
pose the two first premisses, for this transposition gives a 
major with a universal subject ; and in all syllogisms of the 
first figure the major must be universal ; for if this were not 
the case, the middle term would be taken twice particularly. 
Hence all the intermediate premisses of a sorites must serve 
as premisses to universal conclusions. 

In explanation of the third rule, viz., that if the first propo- 
sition be particular, the conclusion must be particular, it may 
be stated, that since the subject of the first proposition in a 
sorites is also the subject of the conclusion, and since no term 
can be used more universally in the conclusion than in the 
premisses, the subject of the conclusion must be particular, 
and consequently the conclusion itself. These conditions 
apply of course only to the categorical sorites. 

A sorites may also be drawn in the conditional or hypo- 



216 MANUAL OF LOGIC. 

thetical form. In the constructive conditional sorites, the 
process is from the position of the first antecedent to the posi- 
tion of the last consequent. 

Example 1. 

If it is the duty of a parent to take care of his children, he 
should keep them as much as possible from vice. 

If he should keep them from vice, he ought to teach them 
what is virtuous. 

If he ought to teach them what is virtuous, he is bound to 
instruct them in religious knowledge. 

But it is the duty of a parent to take care of his children ; 
therefore, 

He is bound to instruct them in religious knowledge. 

Example 2. 

If the scriptures are the word of God, it is important that 
they should be well explained. 

If it be important that they should be well explained, they 
deserve to be diligently studied. 

If they deserve to be diligently studied, an order of men 
should be set apart for that purpose. 

But the scriptures are the word of God ; therefore, 

An order of men should be set apart for diligently studying 
them. 

In the destructive sorites, on the other hand, we proceed 
from the remotion of the last consequent to the remotion 
of the first antecedent. 

Example 1. 

If Romish councils speak truth, Popery should be credited. 

If Popery should be credited, Protestantism is fallacious. 

If Protestantism be fallacious, the scriptures are not the 
rule of faith. 

But the scriptures are the rule of faith ; therefore, 

Romish councils do not speak the truth. 



manual of logic. 217 

Example 2. 
If the soul is material, it must have extension. 
If it has extension, it must have parts. 
If it has parts, it must be dissoluble. 
But the soul is not dissoluble ; therefore, 
The soul is not material. 

If the propositions in a soritical series be metaphysically 
true, and the connection between them strictly just, this sort 
of reasoning will be legitimate ; but it is frequently very 
sophistical, as will appear from the following humorous sorites, 
said to be used by Themistocles, to prove that his son go- 
verned the world : — 

My son governs his mother. 

His mother governs me. 

I govern Athens. 

Athens governs Greece. 

Greece governs the world ; therefore, 

My son governs the world. 

The sorites invented by Goclenius, and hence called the 
Goclenian sorites, differs from the common form in two re- 
spects — 1. Its premisses are reversed; and, 2. It begins with 
the premiss containing the two terms which have the greatest 
extension, while the common form starts with the premiss 
containing the terms which have the greatest intension or 
comprehension. 

The Goclenian sorites may be represented by the following 
symbols : — 

D is E. 
CisD. 
BisC. 
AisB. 
AisE. 

K 



218 MANUAL OF LOGIC. 

(Note.) 

Aristotle does not notice the sorites as a distinct species of argumentation, 
but its principle may be gathered from his writings. — See Categ. 3, 1, and 
Anal. Pr. 1, 25, 2, 11. Its detailed exposition, as a distinct form of reason- 
ing, should properly be attributed to the Stoics. 

The sorites was a favourite mode of argument with Cicero, although in many 
instances with questionable conclusiveness. The following are selected as 
examples : — 

Example 1. 

Quoniamque duos beatissimos esse constat, beatus autem, esse sine virtute 
memo potest, nee virtus sine ratione constare, nee ratio usquam inesse, nisi in 
hominis flgura ; hominis esse specie deos confitendum est. — De Nat. Deor. 1, 
sect. 18. 

Example 2. 

Necesse est, qui fortis sit, eundem esse magni animi ; qui magni animi sit, 
invictum ; qui invictus sit, eum res humanas despicere atque infra se positas 
arbitrari ; despicere autem memo potest eas res propter quas segritudine affici 
potesc. Ex quo efficitur fortem virum segritudine nunquam affici. — Tus. Dis. 
lib. iii. sec. 18. 



SECTION IX. 

OF THE EXAMPLE. 

In the species of argument called example* we draw a 
conclusion from a single fact or occurrence — in other words, 

a The example conceals a defective syllogism, and yet there is no argument 
so commonly employed. ' The French Kevolution of 1 792 will end in an ab- 
solute monarchy, because the English Revolution of 1640 did so.' Such 
reasoning is only valid, provided we can conclude, from the fate of the English 
Revolution, that a?? revolutions lead to absolute monarchy — a judgment which 
may be true in itself, but cannot be formally concluded from the given premiss. 
We require other comparisons and arguments, to show that the tendency to ab- 
solute monarchy is an inseparable mark of revolution, and not a mere accident 
belonging to the English Revolution only. And yet examples are so suggestive, 
that they often appear almost to amount to demonstration ; and it would be 
absurd to endeavour to expel them from rhetoric, or from science, on the ground 
that they are not formally complete. — Outline of the Laws of Thought, p. 335. 

The example differs from induction in two respects — First, Induction proves 
the universal from a complete enumeration of the individuals ; example selects 
single cases. Second, Induction stops at the universal ; example infers syllo- 
gistically a conclusion regarding another individual. — Mansel, p. 82. 



MANUAL OF LOGIC 2] 9 

we infer from a fact that has occurred, that a similar result 
will take place in respect to some other unknown fact or oc- 
currence. 

Example has some relation to induction, but it differs from 
it in two respects — 1. In induction the enumeration must 
consist of many singular facts, while example requires no 
more than one. 2. In induction the conclusion is universal, 
but in example singular. 

In induction the nature of the process is such, that when 
we draw a conclusion we infer that in similar circumstances 
the same result will always follow. In example this is not 
the case, for the conclusion does not infer the certainty of any 
fact occurring in the same manner as the individual fact or 
facts from which we draw our conclusion, but merely the 
'probability of such a result or occurrence. 

Examples. 

1. The civil war between Marius and Sylla rent the re- 
public ; therefore, the war between Pompey and Caesar will 
rend it. 

2. Artabanus employs this argument to dissuade Xerxes 
from his intended invasion of Greece : — 

1 It was I that advised your father, and my brother Darius, 
not to carry arms against the Scythians — men who have no 
cities in any part of their territory ; but he, cherishing the 
hope of subduing those pastors, heeded not my counsel. He 
proceeded on the expedition, and returned, after losing many 
men of his army. But you, my liege, are about to carry war 
against men far more brave than the Scythians — men who 
are reported to be most valiant both by sea and land. It is 
right I should inform you of the danger that we are to appre- 
hend in so doing.' — Herod. Book, 7-10. 

3. I, O king, who have already beheld numerous and 
mighty powers overthrown by smaller, would not fain permit 
you in all things to give way to youth — knowing what an 



220 MANUAL OP LOGIC* 

evil thing it is to covet much — recollecting, likewise, what 
was the unfortunate result of Cyrus' expedition against the 
MassagetaB — calling likewise to mind that of Cambyses against 
the Ethiopians, and having myself with Darius fought the 
campaign against the Scythians, — aware of all these things, I 
held the opinion, that if you did not stir, you would be held 
the happiest of mortals. — Herod. Booh, 7-18. 



SECTION X. 

OF SOPHISMS. 

Sophisms are of two kinds — verbal and material. In the 
former, the fallacy is in the diction ; in the latter, the fallacy 
lurks in the object-matter. In the language of the schools, 
these were termed fallacies in dictione and extra dictionem, 
corresponding with the Aristotelic division, viz., 0/ <raga rqv 
Xs^/y, and 61 i^co 7r\c Xs^sojg. 

Fallacies in the expression are necessarily and essentially 
connected with language. Fallacies in the matte?', on the 
other hand, are related to language only in a secondary or 
accidental sense. a 

Fallacies have been defined to be ' deceptive or apparent 
arguments, by which a man is himself convinced, or endeavours 
to convince others of something which is not really proved.' 

Aristotle enumerates thirteen different kinds of fallacies. 
Of these six are said to be in dictione, or in the expression, 
and seven extra dictionem, or in the matter. This enumera- 
tion is not given as exhaustive of all the possible species of 
fallacies, but rather as a catalogue of the forms under which 
fallacies most generally present themselves in dialectics or 
probable reasoning. 

a The former arise from defects in the arbitrary signs of thought ; and hence 
are frequently confined to a single language. The latter are in the thought 
itself, whether materially in the false application of notions to things, or formally 
in the violation of the laws by which the operations of the reason should be 
governed. Under this head are thus included both false judgments and illogical 
reasonings. — Mansel. 



MANUAL OF LOGIC. 



221 



I. 

FALLACIES IN DICTIONE, OR IN THE EXPRESSION. 

The fallacies in the expression are the following : — 

1. Homonymia, or quibble. 

2. Amphibolia, or ambiguity. 

3. The fallacy of composition, 

4. The fallacy of division. 

5. The fallacy of accent or prosody. 

6. The fallacy of figure of speech. 

1. A sophism of homonymia, or cequivocatio, is when any 
term in the syllogism can be used equivocally, or in a double 
sense, and thus constitute in reality two terms, thereby intro- 
ducing four terms into the syllogism. 

This species of fallacy is too obvious to be employed in a 
process of reasoning. No one can be deceived by it. The 
following may suffice as examples : — - 

1. 

All that believe shall be saved. 
The devils believe ; therefore, 
The devils shall be saved. 

2. 
The dog is an animal. 
Sirius is the dog ; therefore, 
Sirius is an animal. 

3, 
The turtle sings. 
The turtle is a fish ; therefore, 
A fish sings. 

It may not be out of place here to enumerate some of the 
circumstances under which words may have double meanings. 
1. By accident, as light meaning the contrary to heavy and 
also to dark. 2. From analogy, as line in the military or 
naval art, signifying a form of drawing up troops or ships ; 
in geography, a certain division of the earth; in mathematics, 
the shortest distance between two points ; in fishing, a string 



222 MANUAL OF LOGIC. 

to catch fish ; in morals, a rule of conduct ; or, more gene- 
rally, as we term that a sweet taste which gratifies the palate, 
or a sweet sound which gratifies the ear ; so in like manner 
the leg of a table, the leg of an animal; the foot of a mountain, 
the foot of a man. 3. From resemblance, as a blade of grass 
from its resemblance to the blade of a sword ; dove- tail in 
joinery, from its similarity to the tail of a dove. 4. From 
metaphor, as a ship ploughing the deep. 

2. Amphibolia. In this species of fallacy the ambiguity does 
not arise so much from the double meaning of a word as from 
the various constructions of which a sentence is capable. The 
ancient languages, and more particularly the Greek and 
Latin, are liable to a variety of construction, from the in- 
flexions of the words, and the inverted nature of the sen- 
tences. Thus, in the well-known example given by Wallis — 

Aio te -ZEacida, Romanum vincere posse, (I say, the Ro- 
man you shall kill) — 

it does not appear, from the form of the expression, whether 
.ZEacides was to slay the Roman, or the Roman JEacides. 

3. Fallacy of Composition. This fallacy occurs when the 

middle term is used distributively in the major premiss, and 

collectively in the minor ; for in this case we argue from a 

term first taken in its divided sense, and then in its collective 

sense, e. g. — 

1. 

Three and two are two numbers. 

Five is three and two ; therefore, 

Five is two numbers. 

2. 

The testimony of this witness is insufficient to prove the 
fact alleged — so is the testimony of that witness — and so of 
the other. 

We believe the fact on the testimony of this, that, and the 
other witness. 

Therefore, we believe the fact on sufficient evidence. 



MANUAL OF LOGIC. 223 

The gaining of a high prize is no uncommon occurrence. 
What is of no uncommon occurrence may be reasonably 
expected. 

The gaining of a high prize may be reasonably expected. 

4. Fallacy of Division. This fallacy is the converse of that 
of composition. It occurs when the middle term is used 
collectively in the major premiss, and distributively in the 
minor — there being no legitimate inference from a term used 
in a collective sense in one premiss, and in a distributive 
sense in another, e. g. — - 

1. 

The primary planets are seven. 

Mercury and Venus are primary planets ; therefore, 

Mercury and Venus are seven. 
2. 

All the apples from that tree are worth twenty shillings. 

This is an apple from that tree ; therefore, 

It is worth twenty shillings. 

3. 

All the angles of a triangle are equal to two right angles. 
A B C is an angle of a triangle ; therefore, 
A B C is equal to two right angles. 

4. 
All the trees make a thick shade. 
This is a tree ; therefore, 
It makes a deep shade. 

5. Fallacy of Accent or Prosody. A fallacy of accent 
or prosody is when the same thing is predicated of different 
terms, if they be only written or pronounced in the same 
way, e. g — 

Equus est quadrupes. 
Aristides est JEquus. 
Aristides est quadrupes. 

The play of words here is upon ' equus ' and ' sequus,' and 



224 MANUAL OF LOGIC. 

is nothing but a sorry pun, as all examples of this fallacy 
must necessarily be. 

6. Fallacy of the Figure of Speech. This fallacy arises 
from words nearly related to one another, by etymology or 
the grammatical structure of language. Many words springing 
from the same root may have such a similarity of sound, 
although varying in signification, as to make them appear to 
be identical in meaning. Such are murder, murderer ; pro- 
ject, projector; presume, presumption; art, artful; design, 
designing ; faith, faithful ; theory, theorist, &c. The fol- 
lowing are examples : — 

Murder should be punished with death 

This man is a murderer. 

This man should be punished with death. 

However just in this case the conclusion may be, the syllo- 
gism cannot properly be called an argument, for the term 
' murder ' is certainly not a proper middle term, to contain 
the minor term ' murderer.' 

Projectors are unfit to be trusted. 
This man has formed a project. 
This man is unfit to be trusted. 

This argument is also invalid, for the bad sense usually attach- 
ed to the word ' projector' is not implied in the term * project.' 

Theorists are unsafe guides. 

This man has formed a theory ; therefore, 

He is an unsafe guide. 

The fallacy in this example lies in inferring, that a person 
who frames a theory must be a theorist. The two terms, 
though derived from the same root, cannot be considered as 
equivalent expressions, for the meaning commonly attached 
to the latter term is not implied in the former. To frame a 
theory is considered a proof of intellectual skill ; but to be a 
theorist, in the common acceptation of the term, implies a 
proneness to unsound speculation. 



MANUAL OF LOGIC. 225 

II. 

FALLACIES EXTRA DICTIONBM, OR IN THE MATTER. 

Material fallacies, as the name implies, do not arise from 
any ambiguity in terms or forms of speech ; and to this class 
may therefore be referred any species of fallacy not resulting 
from ambiguity of language. Some are of opinion that mate- 
rial fallacies are the only ones that should be designated 
strictly logical, while others (the formal school of logicians) 
consider them as beyond the province altogether. The fal- 
lacies in the matter are the following : — 

1. Fallacia accidentis. 

2. Fallacia a dicto secundum quid ad dictum simpliciter, or 
its converse — fallacia a dicto simpliciter ad dictum secundum 
quid. 

3. Ignorationis elenchi. 

4. A non causa ut causa. 

5. Fallacia consequentis. 

6. Fallacia petitionis principii. 

7. Fallacia plurium interrogationum. 

1. Fallacia Accidentis. 
i The fallacia accidentis 2 - arises when one of the terms 
agrees or disagrees necessarily with the middle term, and the 
other only accidentally ; and yet in the conclusion the terms 
are inferred to agree or disagree necessarily; in other words' 
the middle term is used in one premiss, to signify something 

a The fallacia accidentis occurs when to one of two connected things some- 
thing is attributed which agrees only with the other accidentally. — Saunderson. 

Wallis and Aldrich define it thus : ' When something accidental is confounded 
with that which is essential or principally intended.' 

' The example of this fallacy given by Aristotle is, Coriscus is different from 
Socrates. Socrates is a man ; therefore, Coriscus is different from a man. The 
fallacy lies in assuming, that whatever is different from a given subject is in- 
compatible with all the predicates of that subject. The reasoning is thus illo- 
gical : — Socrates is a man ; Coriscus is not Socrates ; therefore, Coriscus is not 
a man.' — Mansel. 

K 2 



226 MANUAL OF LOGIC. 

simply, and as to its essence, while in the other certain 
accidents are taken into account along with it. 

The following is one of the instances commonly quoted : a — 

What is bought in the market is eaten. 

Raw meat is bought in the market ; therefore, 

Raw meat is eaten. 

In the major premiss the middle term, * bought in the 
market/ must be understood simply as to its substance, while 
in the minor it is used as connected with circumstances and 
accidents. Hence there are four terms. In the following 
example there are also four terms : — 

We are forbidden to kill. 

Using capital punishment is killing. 

We are forbidden to use capital punishment. 

In this example it is plain that the middle term, i kill,' in 
the major proposition, must be understood as referring to the 
divine command, prohibiting violence against human life, and 
that the violence is consequently of a private nature. In the 
minor, on the other hand, the middle must be understood in a 
public or judicial sense, and that circumstances are attached 
to it which make it a middle term, altogether different from 
that used in the major ; yet, in the conclusion, the inference is 
falsely drawn from the one to the other. 

The fallacia accidentis may be refuted either by distin- 
guishing the different senses in which the middle is taken, so 
as to show that there are four terms in the syllogism, or by 
showing that the conclusion is universal, while the minor is 
particular, e. g. — 

Whatever destroys men ought to be prohibited. 
Wine destroys men ; therefore, 
Wine ought to be prohibited. 

Quod emisti comedisti, Crudum emisti ; Ergo Crudum comedisti : in quo 
quod emisti et qual emisti confunduntur ; uade quatuor termini. — Wallis. 



MANUAL OF LOGIC. 227 

In this example it is obvious that an accidental circum- 
stance is confounded with an essential one. The major pro- 
position must mean i Whatever necessarily destroys men ;' 
otherwise it is not true. The minor must mean, ' "Wine acci- 
dentally destroys men ;' and hence there are four terms. 

2. Fallacia a dicto secundum quid ad dictum simpliciter. 

This fallacy occurs when a term is used in one premiss in 
a limited and in the other in an unlimited sense, or, in other 
words, when we reason from a statement made under a cer- 
tain restriction or limitation to the same statement made 
without restriction or limitation. 8. 

It is sometimes difficult to distinguish this fallacy from the 
fallacia accidentis ; and for this reason they have by some 
been regarded as one and the same. In reality, the only 
difference between them is, that in the fallacia accidentis the 
fallacy lurks invariably in the major, while in the fallacy 
under consideration and its converse, it may occur in either 
the major or minor. 

3. Fallacia Ignorationis Elenchi. 
By this form of fallacy is meant the fallacy of a false con- 
tradictory, and we are to understand by it any conclusion 
which seems to be the contradictory of some other conclusion, 
while in fact it is not. Elenchus properly signifies a conclu- 
sion contradictory of an opponent's position, which in every 
disputation is the thing of course to be established. This 
fallacy occurs whenever a disputant either intentionally or 
through ignorance overlooks some one or other of the condi- 
tions necessary for proving the contradictory of any proposi- 

a ■ This fallacy arises when that which is true only restrictedly (secundum 
quid) is taken as simply and absolutely true.' — Saunderson. 

1 When what is laid down in a limited and conditional sense is applied as if 
laid down absolutely.' — Wallis. 

' When we proceed from a term taken in a determinate sense to the same 
taken absolutely.' — Aldrich. 



228 MANUAL OF LOGIC. 

tion laid down ; and as four conditions are required to consti- 
tute a valid contradiction — viz., that we speak of the same 
thing in the same sense, as to the same part, compared with 
the same thing, and existing at the same time — the absence of 
any of these requirements will vitiate a contradictory. 

Examples. 

1. The point in dispute between primitive Christians and 
Polytheists was whether there was one God only, or many 
gods. Lymachus argues that their ancestors adored a plu- 
rality of gods, and were always victorious, which was quite 
foreign to the subject debated. Besides the nations they 
conquered, were also Polytheists. 

2. Paschal, in arguing against Atheists, insists that Atheism 
is more dangerous than Theism ; whereas the point in dispute 
is truth, and not the prudence of either system. 

3. Anger has been called a short madness; and people of 
the weakest understandings are the most subject to it. It is 
remarkable, that when a disputant is in the wrong, he tries to 

make up in violence what he wants in argument. This arises 
from his pride. He will not own his error ; and because he 
is determined not to be convicted of it, he falls into a passion. 
In this example, instead of going to show why anger has 
been called a short madness, the writer shifts his ground, and 
wanders into reflections which have no necessary connection 
with the particular proposition. 

4. A Non Causa* ut Causa. 

By this is meant that fallacy which attributes an effect to a 

a The causes sometimes assigned are unsatisfactory, rather than false — the 
error consisting not in the assignment of & false cause, but of one too general to 
convey any instruction, and thus deceiving the inquirer. For instance, assigning 
the will or permission of God, as the cause of any event, this everybody knows 
already ; but as God always acts by the intermediation of secondary causes, 
it is the intermediate and not the remote cause that is sought, as this alone 
conveys any new knowledge. — Kirwan, p. 460. 



MANUAL OF LOGIC. 229 

false cause. It is sometimes divided into the fallacy a non 
vera pro vera, and the fallacy a non tali pro tali, e. g., < A 
comet has appeared ; therefore, there will be war. What in- 
toxicates should be prohibited ; and wine intoxicates ; there- 
fore, it should be prohibited/ 

The ancients attributed the damage done by lightning to a 
hard substance, which they called a thunderbolt, because they 
were unacquainted with the nature of the electric fluid, 
and supposed that the small substances, such as a part of a 
brick or stone, which were frequently found vitrified where 
the electric fluid struck, really came from the clouds. 

5. Fallacia Consequentis. 

A sophism of a false consequence occurs when there is de- 
duced from a proposition a conclusion which does not follow 
it. This fallacy appears most commonly in the form of an 
enthymeme ; for one of the premisses is suppressed, that it 
may not be immediately evident that the rules are violated, 
e. g., l Crispus is courteous ; therefore, he is a flatterer.' 
When the suppressed premiss is supplied, the syllogism will 
stand either thus : — 

Every flatterer is courteous. 
Crispus is courteous ; therefore, 
Crispus is a flatterer, 

and the first rule of the second figure is violated, or it must 
be its simple converse, viz. — 

Every courteous person is a flatterer, 

and then the rules of conversion are violated. It is refuted 
by adducing the rule which is transgressed, 

6. Fallacia Petitionis Principii, 
Or begging the question, is when that is assumed for granted 



230 MANUAL OF LOGIC. 

which ought to have been proved, or by reasoning in a circle, 
i. e., when the disputant tries to prove reciprocally the conclu- 
sion from the premisses, and the premisses from the conclu- 
sion. 

OF THE PETITIO PEINCIPII. 

Examples. 

1. Pride is odious, because it is disliked by all ; for it pro- 
duces universal hatred. 

2. The Jews argued that Jesus could not be the Messiah, 
because he did not appear as a victorious prince, as the pro- 
phecies announced he should, taking for granted that the 
prophecies should be understood in the literal sense, which is 
the point denied by Christians — not only because of the 
miracles of Christ, which proved him plainly to be the Mes- 
siah, but because the literal accomplishment of the prophecies 
could occasion no change of the depraved moral state of the 
world ; and therefore could not be the true sense of these 
prophecies. 

3. When necessarians say that the mind is influenced by the 
preponderant motive, if any motive appeared to be so before, 
as well as after election, their position would be just. But 
they infer the preponderance of the motive before election, 
from its appearance after the election, to have been that with 
which the will complied — an inference which is merely a 
petitio principii, assuming that for true which their opponents 
deny. 

ARGUING IN A CIRCLE. 

Examples. 
1. Sceptics argue that we ought to doubt of everything 
because human reason is fallible, and may deceive us. And 
since reason may deceive us, we should doubt the validity of 
the reasons that induce us to doubt. 



MANUAL OF LOGIC. 231 

2. Aristotle asserts that the stars seem to twinkle, on ac- 
count of their immense distance, and asserts also that they are 
immensely distant, because they seem to twinkle. 

3. Descartes endeavoured to prove that God exists, be- 
cause existence is contained in the clear and distinct idea 
which we have of the Supreme Being ; but he afterwards 
derives the certainty we have, that such ideas cannot deceive 
us from the incompatibility of such deception with the good- 
ness of the Divine Being. 

4. The whole of Dr Brown's elaborate lectures on the 
nature of virtue amounts to nothing more than a vicious circle. 
We approve of actions, because they are right ; and they are 
right, because we approve of them. 

5. The famous arguments of the Romanists, who prove 
the scriptures from the authority of the church, and the 
church from the authority of the scriptures, is a vicious circled 

6. It is certain that wealth often makes the mind uneasy, for 
it tends to fill it full of care ; and it is equally certain that it 
fills it full of care, for wealthy men are seldom at ease in their 
minds. 

a It may be of advantage to the learner to understand the exact grounds on 
■which this argument is to be considered as an instance of a vicious circle. The 
matter is well stated by Dr Kirwan, p. 442 : ' It is commonly said that Catho- 
lics form a vicious circle when they prove the authority of their church by the 
authority of the scriptures, and the authority of the scriptures by that of their 
church. But, in fact, the authenticity, and, consequently, the authority of the 
scriptures is proved by the testimony of Christians of all sects, that is, of all 
those who professed Christianity since the apostolic age unto the present day ; 
and, undoubtedly, the Eoman and Greek Catholics have their share in this tes- 
timonial authority, which should be carefully distinguished from doctrinal 
authority. And as the doctrinal is not proved by the testimonial authority, nor 
the testimonial by the doctrinal, there is no circle or reciprocation of proofs. 
But, if the doctrinal authority of the scriptures were attempted to be proved by 
the doctrinal authority of the church, and the doctrinal authority of the church 
by that of the scriptures, then there would be a circle.' 1 



232 MANUAL OF LOGIC. 

7. Fallacia plurium interrogationum. 

This fallacy occurs when two or more questions, requiring 
each a separate answer, are proposed as one ; so that if one 
answer be given, it must be inapplicable to one of the parti- 
culars asked, e.g., ' Was Pisistratus the usurper and scourge 
of Athens?' The answer, 'No,' would be false of the 
former particular, and 'Yes' would be false of the latter. 
This fallacy is overthrown by giving to each particular a 
separate reply. 

OF INDUCTION. 

The term induction (swaywyjj, inductio) has been variously 
explained. By some it has been understood to mean the in- 
ducing or influencing effect the nature of the reasoning im- 
plied in the inductive process has on the mind of a hearer. 
Others have explained it as a bringing in, as an inference of 
the question to be proved ; while a third class have held it to 
signify a collection or accumulation of instances, to constitute 
an antecedent or premiss, from which to infer a required 
conclusion. 

The last view is the correct one ; for whatever diversity of 
opinion may prevail, regarding the exact nature of the induc- 
tive inference, in one point all must agree, that in the induc- 
tive, argument the inference is from the particular to the uni- 
versal — in other words, from the aggregate of individuals to 
the universal whole constituted by them. 

But to pass from the name to the thing signified by it, 
three conflicting views of the proper function of induction 
present themselves : — 

1. The objective process of investigating particular facts, as 
preparatory to illation or inference. 

To this it is objected, by those who adopt the formal defi- 
nition of logic, that induction, in so far as it is a logical pro- 
cess at all (and it is only logical, in so far as it is formal), is 
equally formal with syllogism, though proceeding in the in- 



MANUAL OF LOGIC. 233 

verse order. And it is objected, farther, that as the investi- 
gation of particular facts is purely an inventive process, it is 
beyond the bounds of a critical science, and cannot be ad- 
mitted within the province of logic. 

2. A material illation or inference of the universal from 
the singular, warranted either by the general analogies of 
nature, or by special presumptions afforded by the object- 
matter of any real science. 

To this view the formal school also object, on the ground 
that the consequence is not logical, for the inference is effected 
vi materia, in virtue of the matter — that is, on grounds not 
implied in the notion of its antecedent. 

3. A formal illation or inference of the universal from the 
individual, as legitimated solely by the laws of thought, and 
abstracted from the conditions of any particular matter. 

This is the formal view, according to which any inference, 
strictly logical in its character, whether inductive or deduc- 
tive, is determined ratione formce, by reason of the form of 
the argument, which signifies that the conclusion is neces- 
sarily implied in the very conception of the premisses, for 
logic recognises no inference that is not necessitated by the 
laws of thought ; and it must therefore be presumed that the 
induction is perfect, i. e., that the individuals mentioned are 
in reality the whole constituents of the species before the 
inductive inference can come in any way within the province 
of the logician. 

To extend the province of logic to the selecting and testing 
of instances, would require a broader definition for the in- 
ductive process than for the deductive. A complete enu- 
meration of instances, or of the members of a class, will con- 
stitute a foundation for a valid inductive inference, but the 
completeness is the result of a material, not of & logical inquiry. 
The Baconian induction, from being more scientific and scru- 
tinising, has superseded the ancient induction per enumera- 
tionem simplicem, but both were merely material inquiries, 



234: MANUAL OP LOGIC. 

and consequently extralogical. Logic has no connection 
with the one or the other beyond the inference deduced from 
their assumed completeness. 

The distinction between deductive and inductive reasoning 
is thus : In deductive reasoning the process is from the whole 
to the parts ; in inductive reasoning, on the other hand, the 
process is from the parts to the whole. 

Deductive reasoning is governed by the rule ; what be- 
longs, or does not belong to the containing whole, belongs or 
does not belong to each and all of the contained parts. In- 
ductive reasoning, again, is governed by the rule ; what be- 
longs, or does not belong, to all the constituent parts, belongs, 
or does not belong to the constituted whole. These two rules 
are equally absolute, and determine all formal or logical in- 
ference. Whatever transcends or violates either of them, 
transcends or violates logic. It would not be less illegitimate 
to infer, by the deductive syllogism, an attribute belonging to 
the whole, of something it was not conceived to contain as 
a part,, than by the inductive to conclude of the whole, what 
is not conceived as a predicate of all its constituent parts. 
Logical inference is thus only of two kinds : it must proceed 
either from the whole to the parts, or from the parts to the 
whole ; and it is only under the character of a constituted or 
containing whole, or of a constituting or contained part, that 
anything can become the term of a logical argumentation . 

As processes of reasoning, deduction and induction are 
equally essential. They are so related, indeed, that the one 
requires the other. Deduction is only possible through in- 
duction. The chief value of the latter consists in realising 
the possibility of the former. Our knowledge commences 
with the apprehension of singulars ; and it is upon the know- 
ledge thus acquired that every universal whole, whatever its 
nature may be, is founded. Deductive reasoning is conse- 
quently not an original process. In the inductive mode, 
logic, by synthetic illation, ascends to its wholes, and in the 
deductive, illation re-descends from whole to parts. 



MANUAL OF LOGIC. 235 

But the two processes are not similar. The one is the 
counterpart of the other. Their analogies and differences 
can be best exemplified by employing the same symbols in an 
ascent through an inductive syllogism, and a re-descent 
through a deductive. 

Inductive Syllogism. 
X, Y, Z, are A. 

X, Y, Z, are (whole) B ; therefore, 
B is A. 

In this example, X, Y, Z, is the middle term, and being 
the subject of both premisses, the syllogism is apparently in 
the third figure ; but it is only in appearance ; for in the de- 
ductive process the conclusion is invariably particular in syllo- 
gisms drawn in the third figure, whereas in the example 
above given the conclusion is universal ; but a universal con- 
clusion is not valid in the third figure ; for since the minor of 
a syllogism in the third figure must be affirmative, its predi- 
cate must be particular ; and since this predicate must be 
the subject of the conclusion, the conclusion must itself be 
particular. 

To say, therefore, on the standard of the deductive, that 
the inductive syllogism is in the third figure is a mistake, 
and the mistake arises from the ambiguity of the copula or 
substantive verb, which in different relations expresses either 
are contained under or constitute. This may be illustrated 
by Aristotle's example, viz. : — 

Man, horse, mule, are long-lived. 

Man, horse, mule, are the whole class of animals wanting 
bill ; therefore, 

The whole class of animals wanting bill are long-lived. 

Here it is evident that the subject ' man, horse, mule,' 
stands in a very different relation to its predicate in the 
major and in the minor premiss, though in both cases the 
connection is expressed by the same copula. In the major 



236 MANUAL OF LOGIC. 

the copula ' are' expresses that the predicate determines the 
subject as a contained part; in the minor, that the subject 
determines the predicate by constituting it a whole ; thus — 

Long-lived contains man, horse, mule. 

Man, horse, mule, constitute animal wanting bill; therefore, 

Long-lived contains animal wanting bill. 

On comparing Aristotle's example with the statement of 
it immediately preceding, the distinctions between it and the 
syllogisms drawn in the third figure are as follows : — 1. That 
in the minor premiss of the inductive syllogism, the subject, 
instead of being contained under the predicate, in reality 
constitutes it; and, 2. That in virtue of this distinction^ a 
universal conclusion is logically drawn in this form, which is 
illegitimate in the third figure of syllogism. 

The above syllogism, when put in the deductive form, will 
stand thus — 

Deductive. 
Bis A. 

X, Y, Z, are (under) B ; therefore, 
X, Y, Z, are A. 

In the propositions of both the inductive and deductive 
syllogisms, the order of the terms remains unchanged, but 
the order of the propositions themselves are reversed; for 
the conclusion of the inductive syllogism forms the major 
premiss of the deductive. Of the terms the major A is com- 
mon to both ; but the middle term, X, Y, Z, of the inductive 
syllogism, is the minor of the deductive. The minor premiss 
is common to both syllogisms, but its meaning, when em- 
ployed in the deductive syllogism, is different from its mean- 
ing in the inductive. In the inductive, the parts, i. e., the 
subjects X, Y, Z, being conceived as constituting the whole, 
are the determining notion, while, in the deductive the same 
parts being conceived as contained under the whole, are the 
determined notion. 



MANUAL OF LOGIC. 237 

The foregoing explanation of the nature of Induction, in 
its logical aspect, seems sufficient for an elementary treatise. 
Examples and explanations might be multiplied, but the 
same fundamental principle applies equally to any instances 
that might have been adduced. The inventive process, by 
which general * truths are arrived at, is unquestionably one 
of the most valuable occupations in which the human mind 
can be employed. And although, in accordance with the 
view here taken of Induction, any such investigation must 
have been deemed extralogical, still, did space permit, the 
processes by which many of the more important truths in 
the physical sciences have been incontrovertibly determined, 
would have been appended. 



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